Use Cramers method to solve:
x + y = 5
5y + 4x = 37
Check Format
Equation 1 is in the correct format.
Check Format
Equation 2 is in the correct format.
Set up standards equations
Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f.
Find a, b, c in ax + by = c
x + y = 5
a = 1, b = 1, c = 5
Find d, e, f in dx + ey = f
5y + 4x = 37
d = 4, e = 5, f = 37
Step 1, calculate Delta (Δ):
Δ = a * e - b * d
Δ = (1 * 5) - (1 * 4)
Δ = 5 - 4
Δ = 1
Step 2, calculate the numerator for x
Numerator(x) = c * e - b * f
Numerator(x) = (5 * 5) - (1 * 37)
Numerator(x) = 25 - 37
Numerator(x) = -12
Step 3, calculate the numerator for y
Numerator(y) = a * f - c * d
Numerator(y) = (1 * 37) - (5 * 4)
Numerator(y) = 37 - 20
Numerator(y) = 17
Evaluate and solve:
| x = | Numerator(x) | |
| Δ |
| x = | -12 | |
| 1 |
x = -12
| y = | Numerator(y) | |
| Δ |
| y = | 17 | |
| 1 |
y = 17
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?
y = 17
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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