Solving Systems of Equations

Front

What is the solution (x, y) to a system of equations?

Back

The point where the equations intersect.

Front

What does it mean if two lines in a system of equations do not intersect?

Back

It means there is no solution to the system.

Front

How do you solve the system of equations: 2x − 3y = −1 and y = x − 1?

Back

Substitute y in the first equation to find x, then use x to find y.

Front

What is the solution to the system of equations: 2x − 3y = −1 and y = x − 1?

Back

(4, 3)

Front

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

Back

Graph both equations on the same coordinate plane.

Front

What does it mean if two lines in a system of equations intersect at a point?

Back

It means there is one unique solution for the system.

Front

What is the solution to the system of equations: 3x - 2y = 14 and 2x + 2y = 6?

Back

(4, -1)

Front

What is a system of equations?

Back

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

Front

What is the purpose of solving a system of equations?

Back

To find the values of the variables that satisfy all equations simultaneously.

Front

What is the graphical representation of a system of equations?

Back

Lines on a coordinate plane that may intersect, be parallel, or coincide.