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 to graph a system of equations?

Back

It means to plot the equations on the same coordinate plane to find their intersection points.

Front

What is the solution to a system of equations?

Back

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

Front

What type of line is used for inequalities with < or >?

Back

Dashed line.

Front

What type of line is used for inequalities with ≤ or ≥?

Back

Solid line.

Front

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

Back

Substitute the point into each equation; if it satisfies all equations, it is a solution.

Front

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

Back

There is no solution to the system; the lines never intersect.

Front

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

Back

There are infinitely many solutions; the lines overlap completely.

Front

How can you tell if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

Back

A straight line with a slope of 2 and a y-intercept of 1.