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 if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

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

Back

They have an infinite number of solutions because every point on the line is a solution.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

They have one unique solution, which is the point of intersection.

Front

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

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.

Front

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

Back

The lines are parallel and do not 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 y-intercept of a line?

Back

Set x = 0 in the equation and solve for y.