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?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is substitution in the context of solving 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

How do you solve for y in the equation y = 8x + 1?

Back

The equation is already solved for y; you can substitute values of x to find corresponding y values.

Tags

CCSS.HSF.IF.A.2

Front

What is the solution to the system: y = 8x + 1 and y = 6x + 3?

Back

(1, 9)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to the system: y = 3 - x and 3y + x = 5?

Back

(2, 1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a system of equations is consistent?

Back

A system is consistent if it has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system: y = 4x + 1 and y = 2x + 5?

Back

(1, 5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

(6, 9)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6