Algebra 1- Solving Systems by Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system by elimination?

Back

Solving by elimination involves manipulating the equations to eliminate one variable, allowing you to solve for the other variable.

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

How do you determine which variable to eliminate?

Back

You can determine which variable to eliminate by looking for coefficients that can be made equal or opposites through multiplication.

Front

What is the first step in solving a system by elimination?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

If you have the equations 3x + y = -15 and -3x - 4y = 30, which variable will eliminate?

Back

x will eliminate.

Front

Solve by elimination: -9x - 4y = -20 and 5x + 4y = 4. What is the solution?

Back

(4, -4) is the solution.

Front

What do you need to multiply the equation 4x - 3y = 5 by to eliminate x with -8x + y = 20?

Back

Multiply by 2.

Front

Solve by elimination: 4x + 4y = 4 and 3x + 4y = 10. What is the solution?

Back

(-6, 7) is the solution.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.