Enter Simultaneous Equations:

<-- Equation 1
<-- Equation 2

Use the substitution method to solve:

12c + 8t = 34

10c + 7t = 29

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Rearrange Equation 2 to solve for c:

10c + 7t = 29

Subtract 7t from both sides to isolate c:

10c + 7t - 7t = 29 - 7t

10c = 29 - 7t

Now divide by 10:

10c
10
=
  
29 - 7t
10

Revised Equation 2:

c  =  29 - 7t
  10

Plug Revised Equation 2 value into c:

12(c) + 8t = 34

12 * ((29 - 7t)/10) + 8t = 34

((348 - 84t)/10) + 8t = 34

Multiply equation 1 through by 10

10 * (((348 - 84t)/10) + 8t = 34)

10 * (((348 - 84t)/10) + 8t = 34)

348 - 84t + 80t = 340

Group like terms:

-84t + 80t = 340 - 348

-4t = -8

Divide each side by -4

-4t
-4
=
  
-8
-4

t  =  -8
  -4

t = 2

Plug this answer into Equation 1

12c + 8(2) = 34

12c + 16 = 34

12c = 34 - 16

12c = 18

Divide each side by 12

12c
12
=
  
18
12

c  =  18
  12

c = 1.5


What is the Answer?
c = 1.5 and t = 2
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

Simultaneous Equations Calculator Video


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