Use Elimination to solve 2x - y = 16 and x 3y = 1

Enter Simultaneous Equations:

<-- Equation 1
<-- Equation 2

Use the elimination method to solve:

2x - y = 16

x + 3y = 1

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Step 1: Multiply Equation 1 by 1:

1 * (2x-y=16) --> 2x - 1y = 16

Step 2: Multiply Equation 2 by 2:

2 * (x+3y=1) --> 2x + 6y = 2

Step 3: Equation 1 - Equation 2:

2x - 1y = 16 - (2x + 6y = 2)
-(2x + 6y = 2)

-1y - 6y = 16 - 2

Step 4: simplify and solve for y:

-7y = 14

y  =  14
  -7

y = -2

Step 5: Rearrange Equation 1 to solve for x:

2x = 16 - -1y

Divide each side by 2

2x
2
=
  
16 - -1y
2

x  =  16 - -1y
  2

Step 6: Plug y = -2 into equation 1:

x  =  16 - -1(-2)
  2

x  =  16 - 2
  2

x  =  14
  2

x = 7


What is the Answer?
x = 7
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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