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 systems of 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 using substitution?

Back

Isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If a system of equations has no solution, what does that mean?

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 infinitely many solutions?

Back

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

Tags

CCSS.8.EE.C.8A

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

(2, 7) because substituting x=2 gives y=7.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system: 2x + 3y = 6, y = 2 - x.

Back

(0, 2) because substituting x=0 gives y=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