Solving Systems of Equations by Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

Given the equations 3x - 4y = -14 and 3x + 2y = -2, what is the solution?

Back

(-2, 2)

Front

Given the equations 3x = 2y - 7 and 2x - 5y = 10, what is the solution?

Back

(-5, -4)

Front

Given the equations 2x + y = 5 and 4x + 3y = 11, what is the solution?

Back

(2, 1)

Front

Given the equations x + 3y = 5 and x = -6y + 14, what is the solution?

Back

(-4, 3)

Front

Given the equations 3x + 2y = 8 and 5x - y = 4, what is the solution?

Back

(2, 1)