Solving 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?

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 systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Given the equations y = 6x - 11 and -2x - 3y = -7, what is the first step to solve for x using substitution?

Back

Substitute y from the first equation into the second equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If y = 6x - 11, what is y when x = 2?

Back

y = 6(2) - 11 = 1.

Tags

CCSS.HSF.IF.A.2

Front

What is the solution to the system y = 6x - 11 and -2x - 3y = -7?

Back

(2, 1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the solution (4, 3) represent in a system of equations?

Back

It represents the point where the two lines intersect, indicating one solution.

Tags

CCSS.8.EE.C.8B

Front

What is a 'One Solution' system?

Back

A system where the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does a system with 'No Solution' look like on a graph?

Back

The lines are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does a system with 'Infinite Solutions' look like on a graph?

Back

The lines are coincident, meaning they lie on top of each other.

Tags

CCSS.8.EE.C.8A