Systems of Equations (Substitution)

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 using substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

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

Get either variable by itself.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

Solve for x and y: 2y + x = -15, x = 3y

Back

(-9, -3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve for x and y: y = 3 - x, 3y + x = 5

Back

(2, 1)

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

Solve for x and y: 3x + 2y = 16, 7x + y = 19

Back

(2, 5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinite solutions?

Back

The equations represent the same line, so they intersect at infinitely many points.

Tags

CCSS.8.EE.C.8A

Front

How can you check your solution for a system of equations?

Back

Substitute the values of the variables back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6