Solving Systems by Elimination

Front

What is a system of linear equations?

Back

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

Front

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

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

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

Back

The first step is to align the equations and manipulate them (if necessary) so that the coefficients of one variable are opposites.

Front

Given the equations 10 = -8x - 7y and -34 = 8x - 5y, what is the solution?

Back

(-3, 2)

Front

Given the equations 7x + 4y = -6 and -7x - 6y = 30, what is the solution?

Back

(6, -12)

Front

Given the equations -2x - 10y = 22 and 2x + 5y = -12, what is the solution?

Back

(-1, -2)

Front

Given the equations 15x + 5y = -70 and -10x - 5y = 45, what is the solution?

Back

(-5, 1)

Front

Given the equations -3x + 3y = 18 and 5x - 3y = -26, what is the solution?

Back

(-4, 2)

Front

What is the elimination method used for?

Back

The elimination method is used to find the values of variables in a system of equations by eliminating one variable at a time.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form Ax + By = C.