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 that are solved together.

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

Write a system of equations based on the following scenario: The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75.

Back

5q + 2z = 1.32 and 3q + 1z = 0.75

Front

What is the solution to the system: 4x + 9y = 28 and -4x - y = -28?

Back

(7, 0)

Front

What does it indicate if a system of linear equations has one solution?

Back

The two lines represented by the equations intersect at one point.

Front

Solve the system by elimination: -2x - 5y = -15 and x + 8y = 13.

Back

(5, 1)

Front

If two lines are parallel, how many solutions do they have?

Back

None.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The two lines are the same line.

Front

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

Back

Align the equations so that like terms are in the same column.

Front

What do you do if the coefficients of one variable are the same in both equations?

Back

You can subtract one equation from the other to eliminate that variable.