Enter Simultaneous Equations:

<-- Equation 1
<-- Equation 2


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Use the elimination method to solve:

3d + 8i = 64

9d + 7i = 107

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Step 1: Multiply Equation 1 by 9:

9 * (3d+8i=64) --> 27d + 72i = 576

Step 2: Multiply Equation 2 by 3:

3 * (9d+7i=107) --> 27d + 21i = 321

Step 3: Equation 1 - Equation 2:

27d + 72i = 576 - (27d + 21i = 321)
-(27d + 21i = 321)

72i - 21i = 576 - 321

Step 4: simplify and solve for i:

51i = 255

i  =  255
  51

i = 5

Step 5: Rearrange Equation 1 to solve for d:

3d = 64 - 8i

Divide each side by 3

3d
3
=
  
64 - 8i
3

d  =  64 - 8i
  3

Step 6: Plug i = 5 into equation 1:

d  =  64 - 8(5)
  3

d  =  64 - 40
  3

d  =  24
  3

d = 8

Test Your Knowledge?
  1. What are the 3 methods to solve a system of 2 equations?
  2. With the elimination method, what are you trying to eliminate?
Keep Practicing
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?
d = 8
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
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