Graphing Systems of Equations

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 for an ordered pair to be a solution to a system of equations?

Back

An ordered pair is a solution to a system of equations if it satisfies all equations in the system when substituted for the variables.

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the x and y values of the ordered pair into each equation. If both equations are true, then the ordered pair is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What does it mean if two lines intersect at a point on a graph?

Back

If two lines intersect at a point, it means that the ordered pair at that point is the unique solution to the system of equations.

Front

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

Back

If two lines are parallel, it means that there is no solution to the system of equations, as the lines never intersect.

Front

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

Back

If two lines coincide, it means they are the same line, and there are infinitely many solutions to the system.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find at least two points that satisfy the equation, plot them on a coordinate plane, and draw a line through the points.

Front

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

Back

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

Front

What is the slope of the line represented by the equation y = 4x + 5?

Back

The slope is 4.