Use the substitution method to solve:
a + c = 327
4a + 1.50c = 978
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:
4a + 1.5c = 978
Subtract 1.5c from both sides to isolate a:
4a + 1.5c - 1.5c = 978 - 1.5c
4a = 978 - 1.5c
Now divide by 4:
| 4a | |
| 4 |
| = |
| 978 - 1.5c |
| 4 |
Revised Equation 2:
| a = | 978 - 1.5c |
| 4 |
Plug Revised Equation 2 value into a:
1(a) + c = 327
1 * ((978 - 1.50c)/4) + c = 327
((978 - 1.5c)/4) + c = 327
Multiply equation 1 through by 4
4 * (((978 - 1.5c)/4) + c = 327)
4 * (((978 - 1.5c)/4) + c = 327)
978 - 1.5c + 4c = 1308
Group like terms:
-1.5c + 4c = 1308 - 978
2.5c = 330
Divide each side by 2.5
| 2.5c | |
| 2.5 |
| = |
| 330 |
| 2.5 |
| c = | 330 |
| 2.5 |
c = 132
Plug this answer into Equation 1
1a + 1(132) = 327
1a + 132 = 327
1a = 327 - 132
1a = 195
Divide each side by 1
| 1a | |
| 1 |
| = |
| 195 |
| 1 |
| a = | 195 |
| 1 |
a = 195
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?
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 = 195 and c = 132
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?
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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