Use Substitution to solve 10v + 6b = 276 and 5v + 2b = 117

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Use the substitution method to solve:

10v + 6b = 276

5v + 2b = 117

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Rearrange Equation 2 to solve for v:

5v + 2b = 117

Subtract 2b from both sides to isolate v:

5v + 2b - 2b = 117 - 2b

5v = 117 - 2b

Now divide by 5:

Revised Equation 2:

Plug Revised Equation 2 value into v:

10(v) + 6b = 276

10 * ((117 - 2b)/5) + 6b = 276

((1170 - 20b)/5) + 6b = 276

Multiply equation 1 through by 5

5 * (((1170 - 20b)/5) + 6b = 276)

5 * (((1170 - 20b)/5) + 6b = 276)

1170 - 20b + 30b = 1380

Group like terms:

-20b + 30b = 1380 - 1170

10b = 210

Divide each side by 10

b = 21

Plug this answer into Equation 1

10v + 6(21) = 276

10v + 126 = 276

10v = 276 - 126

10v = 150

Divide each side by 10

v = 15

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?

v = 15 and b = 21

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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