Systems of Equations - GRE Subject Test: Math
Card 0 of 16
Solve the system of equations.
Solve the system of equations.
The easiest way to solve this question is to use substitution. Since 
you can replace y for 7x-2 in the other equation.
You should have
.
Distribute the 2 to the parentheses.
Add 4 to both sides of the equation.
Subtract 6x from both sides.
Divide by 8 to get x.
Put 1 back in to either equation for x to solve for y.
The easiest way to solve this question is to use substitution. Since
You should have
Distribute the 2 to the parentheses.
Add 4 to both sides of the equation.
Subtract 6x from both sides.
Divide by 8 to get x.
Put 1 back in to either equation for x to solve for y.
Compare your answer with the correct one above
Solve the system of equations.
Solve the system of equations.
First task is to solve at least one of the equations for y.
Move -3x to the other side by adding 3x to both sides.
Divide by 2 to all the terms in the equation.
Plug this value for y into the other equation.
Distribute the 2.
Add 3x to both sides.
Subtract 19 from both sides of the equation.
Divide by 6.
Plug this back in for x in either equation.
First task is to solve at least one of the equations for y.
Move -3x to the other side by adding 3x to both sides.
Divide by 2 to all the terms in the equation.
Plug this value for y into the other equation.
Distribute the 2.
Add 3x to both sides.
Subtract 19 from both sides of the equation.
Divide by 6.
Plug this back in for x in either equation.
Compare your answer with the correct one above
Solve each system of equations.
Solve each system of equations.
Using the substitution method, set the two systems of equations equal to each other.
Isolate the variable by subtracting 
from both sides of the equation.
To get the value of 
, substitute the value of 
in one of the equations.
is the correct answer.
Using the substitution method, set the two systems of equations equal to each other.
Isolate the variable by subtracting
To get the value of
Compare your answer with the correct one above
Solve each system of equations.
Solve each system of equations.
Using the substitution method, set both systems of equations equal to each other.
Isolate the variable by adding 
to both sides of the equation.
Add 
to both sides.
Divide both sides by 3.
To get the value of y, substitute the value of x in one of the equations.
is the correct answer.
Using the substitution method, set both systems of equations equal to each other.
Isolate the variable by adding
Add
Divide both sides by 3.
To get the value of y, substitute the value of x in one of the equations.
Compare your answer with the correct one above
Solve each system of equations.
Solve each system of equations.
To solve this system of equations, you are given the value of 
.
The second equation is 
So you put the value of 
into the second equation.
Combine like terms.
Add 
to both sides of the equation.
Divide both sides by 
.
Substitute the value of x in one of the equations to get the value of y.
is the correct answer.
To solve this system of equations, you are given the value of
The second equation is
So you put the value of
Combine like terms.
Add
Divide both sides by
Substitute the value of x in one of the equations to get the value of y.
Compare your answer with the correct one above
Solve the system of equations.
Solve the system of equations.
To cancel out the 
terms, multiply 
by 
Then add:
______________________
Plug the value of 
which is 
into one of the equations to get the value of 
.
is the correct answer.
To cancel out the
Then add:
______________________
Plug the value of
Compare your answer with the correct one above
Solve the systems of equations.
Solve the systems of equations.
In order to eliminate the 
terms, first multiply the first equation by 
Then multiply the second equation by 
This will now eliminate the 
terms when added together.
+ 
_________________________
Divide both sides by 
Now substitute the value of 
which is 
to get the value of in one of the the two original equations.
Add 
to both sides of the equation.
Divide both sides by 
is the correct answer.
In order to eliminate the
Then multiply the second equation by
This will now eliminate the
+
_________________________
Divide both sides by
Now substitute the value of
Add
Divide both sides by
Compare your answer with the correct one above
Solve the systems of equations.
Solve the systems of equations.
The first step in solving this system of equations is to remove either the 
term or the 
term. This is done by multiplying the second equation by 
.
Now add these two equations together and the 
terms will be removed.
+ 
_____________________
Divide both sides of the equation by 
Put the value of 
, which is 
, into one of the equations to get the value of 
Add 
to both sides of the equation.
Divide both sides by 
is the correct answer.
The first step in solving this system of equations is to remove either the
Now add these two equations together and the
+
_____________________
Divide both sides of the equation by
Put the value of
Add
Divide both sides by
Compare your answer with the correct one above
Find the value of 
and 
that satisfy the equations:
(1) 
and
(2)
.
Find the value of
(1)
and
(2)
Step 1: Write the two equations, one below another and line up the terms.
----------------
Step 2: We see that we have 
and 
. We can add these two equations up, which will isolate y and let us solve for x.
We add here.
----------------
Step 3: We will isolate x by itself. We need to divide by 2 on both sides to get x.
Step 4: We found x, so we can plug in that value into any one of the two equations and solve for y. Let's choose equation (1).
(1)...
. Isolate y by itself. We are going to subtract 6 from both sides.
. Simplify the left hand side.
Step 5: We will divide by -1 to get the value of y.
The values that solve this system of equations is 
and 
.
Step 1: Write the two equations, one below another and line up the terms.
----------------
Step 2: We see that we have
----------------
Step 3: We will isolate x by itself. We need to divide by 2 on both sides to get x.
Step 4: We found x, so we can plug in that value into any one of the two equations and solve for y. Let's choose equation (1).
(1)...
Step 5: We will divide by -1 to get the value of y.
The values that solve this system of equations is
Compare your answer with the correct one above
Solve this system of equations.
Solve this system of equations.
To solve this system of equations, add. This will eliminate or remove the 
terms.
+
___________________
Divide both sides by 
To get the value of 
replace the variable with the value of that variable in one of the equations.
Subtract 
from both sides of the equation.
Divide both sides of the equation by 
is the correct answer.
To solve this system of equations, add. This will eliminate or remove the
+
___________________
Divide both sides by
To get the value of
Subtract
Divide both sides of the equation by
Compare your answer with the correct one above
Solve this system of equations.
Solve this system of equations.
To solve this system of equations, subtract the second equation from the first.
____________________________
Now, substitute in the value for x into one of the equations to solve for the value of 
.
Now subtract five from each side.
Divide both sides by negative 2:
is the correct answer.
To solve this system of equations, subtract the second equation from the first.
____________________________
Now, substitute in the value for x into one of the equations to solve for the value of
Now subtract five from each side.
Divide both sides by negative 2:
Compare your answer with the correct one above
Solve this system of equations:
Solve this system of equations:
Set both equations equal to each other and solve.
Add 
to both sides of the equation.
Add 
to both sides of the equation.
Divide both sides by 8.
Plug the value of the 
variable into one of the equations to get the value of 
is the correct answer for this system of equations.
Set both equations equal to each other and solve.
Add
Add
Divide both sides by 8.
Plug the value of the
Compare your answer with the correct one above
Solve this system of equations:
Solve this system of equations:
To solve this system of equations, multiply the first equation by 
.
Now add the two equations together to remove the 
terms.
+ 
_____________________________
Divide both sides by 
.
Plug the value of the 
variable, which is 
into one of the equations.
Subtract 
from both sides of the equation.
Divide both sides by 
is the correct answer for this system of equations.
To solve this system of equations, multiply the first equation by
Now add the two equations together to remove the
+
_____________________________
Divide both sides by
Plug the value of the
Subtract
Divide both sides by
Compare your answer with the correct one above
Solve this system of equations:
Solve this system of equations:
To solve this system of equations:
Multiply the first equation by 
and the second equation by 
.
Add these two equations; this will remove the 
terms.
+
___________________
To get the value of 
, plug the value of 
, which is 
into one of the equations.
Divide both sides by 
is the correct answer for this system of equations.
To solve this system of equations:
Multiply the first equation by
Add these two equations; this will remove the
+
___________________
To get the value of
Divide both sides by
Compare your answer with the correct one above
Solve this system of equations:
Solve this system of equations:
To solve this system of equations, set both equations equal to one another.
Add 
to both sides of the equation.
Subtract 
from both sides of the equation.
Multiply both sides of the equation by 
.
Plug the value of 
, which is 
into one of the equations to get the value of 
is the correct answer for this system of equations.
To solve this system of equations, set both equations equal to one another.
Subtract
Multiply both sides of the equation by
Plug the value of
Compare your answer with the correct one above
To answer this question you must first solve for one of the variables. This can be done with either variable with either equation. In this example of how to solve the problem we will solve for y using the second equation
subtract 8x from both sides
divide both sides by y
Now we plug this into the first equation for the y variable
Distribute the 3
Simplify
subtract 9 from both sides
divide by -2 on both sides
Using this we solve for y in the second equation
simplify
add 8 to both sides
divide by 4 on both sides
Final answer
and 
To answer this question you must first solve for one of the variables. This can be done with either variable with either equation. In this example of how to solve the problem we will solve for y using the second equation
subtract 8x from both sides
divide both sides by y
Now we plug this into the first equation for the y variable
Distribute the 3
Simplify
subtract 9 from both sides
divide by -2 on both sides
Using this we solve for y in the second equation
simplify
add 8 to both sides
divide by 4 on both sides
Final answer
Compare your answer with the correct one above