 # Use Substitution to solve g + r = 1197 and 2g + 5.50r = 3577

<-- Equation 1
<-- Equation 2

## Use the substitution method to solve:

g + r = 1197
2g + 5.50r = 3577

Equation 1 is in the correct format.
Equation 2 is in the correct format.

2g + 5.5r = 3577

## Subtract 5.5r from both sides to isolate g:

2g + 5.5r - 5.5r = 3577 - 5.5r
2g = 3577 - 5.5r

## Now divide by 2:

 2g 2
 =
 3577 - 5.5r 2

## Revised Equation 2:

 g  = 3577 - 5.5r 2

## Plug Revised Equation 2 value into g:

1(g) + r = 1197
1 * ((3577 - 5.50r)/2) + r = 1197
((3577 - 5.5r)/2) + r = 1197

## Multiply equation 1 through by 2

2 * (((3577 - 5.5r)/2) + r = 1197)
2 * (((3577 - 5.5r)/2) + r = 1197)
3577 - 5.5r + 2r = 2394

## Group like terms:

-5.5r + 2r = 2394 - 3577
-3.5r = -1183

## Divide each side by -3.5

 -3.5r -3.5
 =
 -1183 -3.5

 r  = -1183 -3.5

r = 338

## Plug this answer into Equation 1

1g + 1(338) = 1197
1g + 338 = 1197
1g = 1197 - 338
1g = 859

## Divide each side by 1

 1g 1
 =
 859 1

 g  = 859 1

g = 859

Solve using Gauss Jordan Elimination

g = 859 and r = 338

### 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?

1. Δ = a * e - b * d

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### 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