Use Substitution to solve 90A + 20B = 13000 and 270A + 30B = 33000

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Use the substitution method to solve:

90A + 20B = 13000

270A + 30B = 33000

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Rearrange Equation 2 to solve for a:

270a + 30b = 33000

Subtract 30b from both sides to isolate a:

270a + 30b - 30b = 33000 - 30b

270a = 33000 - 30b

Now divide by 270:

Revised Equation 2:

Plug Revised Equation 2 value into a:

90(a) + 20b = 13000

90 * ((33000 - 30b)/270) + 20b = 13000

((2970000 - 2700b)/270) + 20b = 13000

Multiply equation 1 through by 270

270 * (((2970000 - 2700b)/270) + 20b = 13000)

270 * (((2970000 - 2700b)/270) + 20b = 13000)

2970000 - 2700b + 5400b = 3510000

Group like terms:

-2700b + 5400b = 3510000 - 2970000

2700b = 540000

Divide each side by 2700

b = 200

Plug this answer into Equation 1

90a + 20(200) = 13000

90a + 4000 = 13000

90a = 13000 - 4000

90a = 9000

Divide each side by 90

a = 100

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?

a = 100 and b = 200

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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