ACCUPLACER Elementary Algebra

ACCUPLACER Elementary Algebra focuses on assessing and enhancing foundational algebra skills essential for success in higher-level mathematics.

Operations with Integers and Rational NumbersSimplifying Algebraic ExpressionsSolving Linear Equations
Solving and Graphing Linear InequalitiesSystems of Linear EquationsPolynomials and Factoring
Budgeting and Shopping MathTravel and Distance ProblemsRecipe Scaling and Proportions
Mastering Multiple Choice QuestionsTime Management During the Test
Operations with Inte...Simplifying Algebrai...Solving Linear Equat...Solving and Graphing...Systems of Linear Eq...Polynomials and Fact...Budgeting and Shoppi...Travel and Distance ...Recipe Scaling and P...Mastering Multiple C...Time Management Duri...
Advanced Topics

Systems of Linear Equations

What is a System of Linear Equations?

A system is two or more linear equations with the same variables. The solution is where the equations intersect—values that satisfy all equations at once.

Methods to Solve

  • Graphing: Draw both lines; where they cross is the solution.
  • Substitution: Solve one equation for a variable, then plug into the other.
  • Elimination: Add or subtract equations to eliminate a variable.

Real-World Example

Systems help solve problems like finding out how many adults and kids attended an event if you know the total number and total cost.

Pro Tip

Always check your solution in both equations!

Examples

  • Solve \( x + y = 10 \) and \( x - y = 2 \); solution: \( x = 6, y = 4 \).

  • Graph \( y = 2x \) and \( y = x + 3 \); they cross at \( (3, 6) \).

In a Nutshell

Find variable values that work in more than one equation at the same time.

Next
Polynomials and Factoring