How to Solve Systems of Equations in Algebra 2

What Are Systems of Equations?

A system of equations is a set of two or more equations with the same variables. In Algebra 2, you typically solve systems with two variables (x and y).

Method 1: Substitution

1. Solve one equation for one variable.
2. Substitute into the other equation.
3. Solve and back-substitute.

Method 2: Elimination

1. Multiply equations to align coefficients.
2. Add or subtract to eliminate one variable.
3. Solve and back-substitute.

Example (Elimination)

Solve: \( 2x + 3y = 7 \) and \( x - y = 1 \)

1. Multiply Eq2 by 3: \( 3x - 3y = 3 \)
2. Add to Eq1: \( 5x = 10 \), so \( x = 2 \)
3. Substitute: \( 2 - y = 1 \), so \( y = 1 \)

Solution: \( (2, 1) \). Try it on our solver!