Graphing Systems of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to intersect?

Back

It means they have one solution, which is the point where they cross.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if two lines are parallel?

Back

They have no solutions because they never intersect.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the intersection point of two lines graphically?

Back

By plotting both lines on a graph and identifying the point where they cross.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, so every point on the line is a solution.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point (0, 3) on the graph.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

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

Back

Graph each equation on the same coordinate plane.