Solving Systems by Graphing

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is slope-intercept form?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert an equation to slope-intercept form?

Back

Isolate y on one side of the equation.

Front

What is the slope of the line represented by the equation y = -4 + (5/3)x?

Back

The slope is 5/3.

Front

What is the y-intercept of the equation y = -4 + (5/3)x?

Back

The y-intercept is -4.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution because the lines never intersect.

Front

What does it mean if two lines are coincident in a system of equations?

Back

It means there are infinitely many solutions because the lines overlap.

Front

How can you determine the solution of a system of equations from a graph?

Back

The solution is the point where the two lines intersect.

Front

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

Back

The solution is (1, -1).