Solving Systems of Equations by Graphing

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations by graphing?

Back

To solve a system of equations by graphing, you graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What does the intersection point of two lines represent in a system of equations?

Back

The intersection point represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines never intersect, which means there is no solution to the system of equations represented by those lines.

Tags

CCSS.8.EE.C.8B

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Tags

CCSS.8.EE.B.5

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.6

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-coordinate.

Front

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

Back

If two lines intersect at a single point, it means there is exactly one solution to the system of equations.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a solution to a system of equations?

Back

The graphical representation of a solution is the point where the graphs of the equations intersect on the coordinate plane.

Tags

CCSS.8.EE.C.8B

Front

How can you check if your solution to a system of equations is correct?

Back

You can check if your solution is correct by substituting the values back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6