Use Substitution to solve x + 2y = 22 and 2x + y = 28

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Use the substitution method to solve:

x + 2y = 22

2x + y = 28

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Rearrange Equation 2 to solve for x:

2x + y = 28

Subtract y from both sides to isolate x:

2x + y - y = 28 - y

2x = 28 - y

Plug Revised Equation 2 value into x:

1(x) + 2y = 22

1 * (28 - y) + 2y = 22

((28 - 1y)/2) + 2y = 22

Multiply equation 1 through by 2

2 * (((28 - 1y)/2) + 2y = 22)

2 * (((28 - 1y)/2) + 2y = 22)

28 - 1y + 4y = 44

Group like terms:

-1y + 4y = 44 - 28

3y = 16

Divide each side by 3

y = 5.3333333333333

Plug this answer into Equation 1

1x + 2(5.3333333333333) = 22

1x + 10.666666666667 = 22

1x = 22 - 10.666666666667

1x = 11.333333333333

Divide each side by 1

x = 11.333333333333

Test Your Knowledge?

1. What are the 3 methods to solve a system of 2 equations?
2. With the elimination method, what are you trying to eliminate?

Common Core State Standards In This Lesson

CCSS.MATH.CONTENT.8.EE.C.8,CCSS.MATH.CONTENT.8.EE.C.8.B

What is the Answer?

x = 11.333333333333 and y = 5.3333333333333

How does the Simultaneous Equations Calculator work?

Free Simultaneous Equations Calculator - Solves a system of simultaneous equations with 2 unknowns using the following 3 methods:
1) Substitution Method (Direct Substitution)
2) Elimination Method
3) Cramers Method or Cramers Rule Pick any 3 of the methods to solve the systems of equations 2 equations 2 unknowns
This calculator has 2 inputs.

What 1 formula is used for the Simultaneous Equations Calculator?

Δ = a * e - b * d

What 7 concepts are covered in the Simultaneous Equations Calculator?

cramers rule

an explicit formula for the solution of a system of linear equations with as many equations as unknowns

eliminate

to remove, to get rid of or put an end to

equation

a statement declaring two mathematical expressions are equal

simultaneous equations

two or more algebraic equations that share variables

substitute

to put in the place of another. To replace one value with another

unknown

a number or value we do not know

variable

Alphabetic character representing a number

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