Solving Systems of Equations by Graphing (PA)

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 graphing?

Back

It means to plot the equations on a graph and find the point(s) where they intersect, which represents the solution(s).

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If both equations are true, the point is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

Front

How do you find the intersection of two lines graphically?

Back

Plot both lines on the same graph and identify the point where they cross.

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect and thus have no solution.

Front

What does it mean if two lines are coincident?

Back

Coincident lines lie on top of each other, meaning they have infinitely many solutions.