Use the elimination method to solve:
90A + 20B = 13000
270A + 30B = 33000
Check Format
Equation 1 is in the correct format.
Check Format
Equation 2 is in the correct format.
Step 1: Multiply Equation 1 by 270:
270 * (90a+20b=13000) --> 24300a + 5400b = 3510000
Step 2: Multiply Equation 2 by 90:
90 * (270a+30b=33000) --> 24300a + 2700b = 2970000
Step 3: Equation 1 - Equation 2:
24300a + 5400b = 3510000 - (24300a + 2700b = 2970000)
-(24300a + 2700b = 2970000)
5400b - 2700b = 3510000 - 2970000
Step 4: simplify and solve for b:
2700b = 540000
| b = | 540000 |
| 2700 |
b = 200
Step 5: Rearrange Equation 1 to solve for a:
90a = 13000 - 20b
Divide each side by 90
| 90a | |
| 90 |
| = |
| 13000 - 20b |
| 90 |
| a = | 13000 - 20b |
| 90 |
Step 6: Plug b = 200 into equation 1:
| a = | 13000 - 20(200) |
| 90 |
| a = | 13000 - 4000 |
| 90 |
| a = | 9000 |
| 90 |
a = 100
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 = 100
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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