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 when a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

How do you solve a system of equations using substitution?

Back

You solve one equation for one variable and substitute 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 by substitution?

Back

Isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you find the solution?

Back

Set 2x + 3 = -x + 1 and solve for x.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the solution (x, y) represent in a system of equations?

Back

It represents the point where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that do not intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations with infinite solutions?

Back

Two overlapping lines that are the same.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.

Tags

CCSS.8.EE.C.8A