Solving Systems of Equations by Graphing

Front

What is a system of linear equations?

Back

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

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that the equations represent the same line, and every point on the line is a solution.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

How do you find the solution to a system of equations by graphing?

Back

You graph both equations on the same coordinate plane and identify the point where they intersect.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.

Front

What is the y-intercept of the line represented by the equation y = -2x + 5?

Back

The y-intercept is 5.

Front

If two lines intersect at a point, what does that indicate about the system of equations?

Back

It indicates that the system has a unique solution.

Front

What is the graphical representation of the equation x = 4?

Back

A vertical line that crosses the x-axis at 4.

Front

What is the graphical representation of the equation y = -3?

Back

A horizontal line that crosses the y-axis at -3.