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 solution to a system of equations?

Back

The point (x, y) where the equations intersect on a graph.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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 substitution method?

Back

A method for solving systems of equations by replacing one variable with an equivalent expression from another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Given the equations y = 2x + 3 and y = -x + 1, how do you solve using substitution?

Back

Set 2x + 3 = -x + 1 and solve for x, then substitute back to find y.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving the system 2y + x = -15 and x = 3y using substitution?

Back

Substitute 3y for x in the first equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If you have the equations 5x - 4y = -3 and y = -3x + 5, how do you solve them?

Back

Substitute -3x + 5 for y in the first equation and solve for x.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6