Use the elimination method to solve:
3p + 4s = 40
5p + 6s = 62
Check Format
Equation 1 is in the correct format.
Check Format
Equation 2 is in the correct format.
Step 1: Multiply Equation 1 by 5:
5 * (3p+4s=40) --> 15p + 20s = 200
Step 2: Multiply Equation 2 by 3:
3 * (5p+6s=62) --> 15p + 18s = 186
Step 3: Equation 1 - Equation 2:
15p + 20s = 200 - (15p + 18s = 186)
-(15p + 18s = 186)
20s - 18s = 200 - 186
Step 4: simplify and solve for s:
2s = 14
| s = | 14 |
| 2 |
s = 7
Step 5: Rearrange Equation 1 to solve for p:
3p = 40 - 4s
Divide each side by 3
| 3p | |
| 3 |
| = |
| 40 - 4s |
| 3 |
| p = | 40 - 4s |
| 3 |
Step 6: Plug s = 7 into equation 1:
| p = | 40 - 4(7) |
| 3 |
| p = | 40 - 28 |
| 3 |
| p = | 12 |
| 3 |
p = 4
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?
p = 4
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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