Systems of Equations: Substitution/Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphing method in solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the point of intersection represents the solution.

Tags

CCSS.8.EE.C.8B

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

Front

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

Back

It means there are infinitely many solutions, as the lines overlap completely.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The form is 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 can you find the y-coordinate of the solution in a system of equations?

Back

By substituting the x-value of the solution into either equation to find the corresponding y-value.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations using substitution?

Back

Isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6