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

Crop Image

×

Crop

Use the substitution method to solve:

g + r = 1197

2g + 5.50r = 3577

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Rearrange Equation 2 to solve for g:

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:

Revised Equation 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

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

g = 859

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?

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?

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

Math is always fascinating! Have you noticed? On the path to discovering the ultimate mysteries of math, we move forward with small steps.
Many such discoveries of mathematical formulas validate the research efforts of those who came before us. If you want to inspire yourself and those around you, try making your own Custom Enamel Badges of achievement for small accomplishments.
These vivid pin badges can be a constant reminder that numbers aren't exactly cold and that they can always be accompanied by fun and hope.