Solving Systems by Graphing (already in y=)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system by graphing?

Back

To solve a system by graphing means to plot each equation on the same graph and identify the point(s) where they intersect.

Front

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

Back

Front

How do you find the slope from an equation in slope-intercept form?

Back

Front

What is the y-intercept of a linear equation?

Back

Front

How do you graph a linear equation in slope-intercept form?

Back

1. Start at the y-intercept (0, b). 2. Use the slope (rise/run) to find another point. 3. Draw a line through the points.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

What is the solution to a system of equations if the lines intersect at one point?

Back

The solution is the coordinates of the intersection point, which satisfies both equations.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines are parallel and do not intersect.