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 substitution mean in the context of systems of equations?

Back

Substitution is 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 = 2x + 3?

Back

To solve for y, simply substitute any value of x into the equation.

Tags

CCSS.HSF.IF.A.2

Front

What is the first step in solving a system of equations using substitution?

Back

Identify one equation and solve it for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If x = 2, what is the value of y in the equation y = 3x - 1?

Back

y = 3(2) - 1 = 5.

Tags

CCSS.HSF.IF.A.2

Front

What is the solution to the system of equations: x + y = 10 and x = 4?

Back

Substituting x = 4 into the first equation gives y = 6, so the solution is (4, 6).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two equations in a system have 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 graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines on a coordinate plane.

Tags

CCSS.8.EE.C.8B

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Set the equations equal: 2x + 1 = -x + 4. Solving gives x = 1, y = 3, so the solution is (1, 3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6