Use the substitution method to solve:
a + b = 88
13a + 17b = 128
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:
13a + 17b = 128
Subtract 17b from both sides to isolate a:
13a + 17b - 17b = 128 - 17b
13a = 128 - 17b
Now divide by 13:
| 13a | |
| 13 |
| = |
| 128 - 17b |
| 13 |
Revised Equation 2:
| a = | 128 - 17b |
| 13 |
Plug Revised Equation 2 value into a:
1(a) + b = 88
1 * ((128 - 17b)/13) + b = 88
((128 - 17b)/13) + b = 88
Multiply equation 1 through by 13
13 * (((128 - 17b)/13) + b = 88)
13 * (((128 - 17b)/13) + b = 88)
128 - 17b + 13b = 1144
Group like terms:
-17b + 13b = 1144 - 128
-4b = 1016
Divide each side by -4
| -4b | |
| -4 |
| = |
| 1016 |
| -4 |
| b = | 1016 |
| -4 |
b = -254
Plug this answer into Equation 1
1a + 1(-254) = 88
1a - 254 = 88
1a = 88 - -254
1a = 342
Divide each side by 1
| 1a | |
| 1 |
| = |
| 342 |
| 1 |
| a = | 342 |
| 1 |
a = 342
Test Your Knowledge?
- What are the 3 methods to solve a system of 2 equations?
- With the elimination method, what are you trying to eliminate?
Keep Practicing
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 = 342 and b = -254
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.
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?
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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