Solving Systems of Equations By Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

Solve by elimination: 2x + 9y = -7 and 6x - 3y = 9

Back

(1, -1)

Front

What do you have to multiply the first equation by to have the x's be opposite and the same? (2x + 9y = -7)

Back

-3

Front

Solve by elimination: -14x - 10y = -18 and 7x + 9y = -23

Back

(7, -8)

Front

Solve by elimination: -9x - 4y = -20 and 5x + 4y = 4

Back

(4, -4)

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by eliminating one variable, making it easier to solve for the other.

Front

When is it appropriate to use the elimination method?

Back

The elimination method is appropriate when the coefficients of one variable can easily be made equal or opposite.

Front

What is the first step in the elimination method?

Back

The first step is to manipulate the equations to align the coefficients of one variable.

Front

If you have the equations 3x + 2y = 6 and 6x + 4y = 12, what can you conclude?

Back

The equations represent the same line, hence they have infinitely many solutions.

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.