Systems of Equations - Substitution

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?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is substitution in the context of solving equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Solve one of the equations for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If you have the equations y = 2x + 3 and 4x - y = 1, how do you use substitution?

Back

Substitute 2x + 3 for y in the second equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The lines represented by 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, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

Solve the system by substitution: 2x + y = 10, y = 3x - 2.

Back

(4, -2)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system by substitution: x + 2y = 8, x = 4 - y.

Back

(4, 2)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.

Tags

CCSS.8.EE.C.8B