Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math

The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply by to get .

Then, we can add to this equation to yield , so .

We can plug that value into either of the original equations; for example, .

So, as well.

By solving one equation for , and replacing in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.

To solve this system of equations, use substitution. First, convert the second equation to isolate .

Then, substitute into the first equation for .

Combine terms and solve for .

Now that we know the value of , we can solve for using our previous substitution equation.

When we add the two equations, the and variables cancel leaving us with:

which means there is no solution for this system.

When we add the two equations, the variables cancel leaving us with:

Solving for we get:

We can then substitute our value for into one of the original equations and solve for :

Multiply the bottom equation by 5, then add to the top equation:

Multiply the top equation by :

Now add:

Multiply the bottom equation by , then add to the top equation:

Divide both sides by

Multiply the top equation by :

Now add:

We are given

We can solve this by using the substitution method. Notice that you can plug from the first equation into the second equation and then get

Add to both sides

Add 9 to both sides

Divide both sides by 5

So . We can use this value to find y by using either equation. In this case, I'll use .

So the solution is

Solve the first equation for :

Substitute into the second equation:

Multiply the entire equation by 2 to eliminate the fraction:

Using the value of , solve for :

Therefore, the solution is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, elimination makes the most sense because our variables have the same coefficient. We can add our equations together to cancel out the

Next, we can divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

We want to subtract from both sides to isolate the

Our point of intersection, and the solution to the two system of linear equations is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, elimination makes the most sense because our variables have the same coefficient. We can subtract our equations to cancel out the

Next, we can divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

We want to add to both sides to isolate the

Then we divide each side by

Our point of intersection, and the solution to the two system of linear equations is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, elimination makes the most sense because our variables have the same coefficient. We can subtract our equations to cancel out the

Next, we can divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

We want to subtract from both sides to isolate the

Then divide both sides by to solve for

Our point of intersection, and the solution to the two system of linear equations is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, elimination makes the most sense because our variables have the same coefficient. We can subtract our equations to cancel out the

Next, we can divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

We want to subtract from both sides to isolate the

Then divide both sides by to solve for

Our point of intersection, and the solution to the two system of linear equations is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, elimination makes the most sense because our variables have the same coefficient. We can subtract our equations to cancel out the

Next, we can divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

We want to subtract from both sides to isolate the

Then divide both sides by to solve for

Our point of intersection, and the solution to the two system of linear equations is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, elimination makes the most sense because our variables have the same coefficient. We can subtract our equations to cancel out the

Next, we can divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

We want to subtract from both sides to isolate the

Our point of intersection, and the solution to the two system of linear equations is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, substitution makes the most sense because the first equation is already solved for a variable. We can substitute the expression that is equal to , into the of our second equation:

Next, we need to distribute and combine like terms:

We are solving for the value of , which means we need to isolate the to one side of the equation. We can subtract from both sides:

Then divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

Our point of intersection, and the solution to the two system of linear equations is

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.

Substitution can be used by solving one of the equations for either or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the form, and then set both equations equal to each other.

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.

For this problem, substitution makes the most sense because the first equation is already solved for a variable. We can substitute the expression that is equal to , into the of our second equation:

Next, we need to distribute and combine like terms:

We are solving for the value of , which means we need to isolate the to one side of the equation. We can subtract from both sides:

Then divide both sides by to solve for

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and values.

Now that we have the value of , we can plug that value into the variable in one of our given equations and solve for

Our point of intersection, and the solution to the two system of linear equations is