## Enter Simultaneous Equations:

<-- Equation 1
<-- Equation 2

3a + 4c = 136

2a + 3c = 97

##### 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

3a + 4c = 136

a = 3, b = 4, c = 136

##### Find d, e, f in dx + ey = f

2a + 3c = 97

d = 2, e = 3, f = 97

##### Step 1, calculate Delta (Δ):

Δ = a * e - b * d

Δ = (3 * 3) - (4 * 2)

Δ = 9 - 8

Δ = 1

##### Step 2, calculate the numerator for a

Numerator(a) = c * e - b * f

Numerator(a) = (136 * 3) - (4 * 97)

Numerator(a) = 408 - 388

Numerator(a) = 20

##### Step 3, calculate the numerator for c

Numerator(c) = a * f - c * d

Numerator(c) = (3 * 97) - (136 * 2)

Numerator(c) = 291 - 272

Numerator(c) = 19

##### Evaluate and solve:

 a  = Numerator(a) Δ

 a  = 20 1

a = 20

#### You have 2 free calculationss remaining

 c  = Numerator(c) Δ

 c  = 19 1

c = 19

#### You have 2 free calculationss remaining

c = 19
##### 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.

### What 1 formula is used for the Simultaneous Equations Calculator?

Δ = a * e - b * d

For more math formulas, check out our Formula Dossier

### 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