Solve Systems of Equations by Graphing

Front

What is a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means there are infinitely many solutions, as every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: same slope and intercept = infinite solutions, same slope different intercept = no solution, different slopes = one solution.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the y-intercept of a linear equation?

Back

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

Front

What is the significance of the point (0,0) in a system of equations?

Back

It is the origin and can be a solution if both equations are satisfied at this point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point, indicating a unique solution for the variables.

Tags

CCSS.8.EE.C.8A