Solve Systems by 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 by substitution?

Back

It means to solve one equation for one variable and then substitute 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 graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

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

Back

It indicates that there is no solution to the system.

Tags

CCSS.8.EE.C.8B

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 intercepts of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in solving the system 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 solve for x?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means the equations represent the same line.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of the solution to a system of equations?

Back

The point where the lines intersect on a graph.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By substituting the solution back into the original equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6