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Sunday, 30 April 2017

Simultaneous equations

 
Sometimes you will be asked to find 2 unknown values by solving 2 equations at the same time. These types of equations are called simultaneous equations.
Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time.
The first step is to try to eliminate one of the unknowns.

Example

Solve these simultaneous equations and find the values of x and y.
  • Equation 1: 2x + y = 7
  • Equation 2: 3x - y = 8
Add the two equations to eliminate the ys:
  • 2x + y = 7
  • 3x - y = 8
  • ------------
  • 5x = 15
  • x = 3
  • Now you can put x = 3 in either of the equations.
  • Substitute x = 3 into the equation 2x + y = 7:
  • 6 + y = 7
  • y = 1
So the answers are x = 3 and y = 1
Question
  • Solve the two equations:
  • Equation 1: 2a - 5b = 11
  • Equation 2: 3a + 2b = 7
toggle answer
We can also use a method of substitution. Look at the following example:

Example

Solve the simultaneous equations:
Equation 1: y - 2x = 1
Equation 2: 2y - 3x = 5
Rearranging Equation 1, we get y = 1 + 2x
We can replace the 'y' in equation 2 by substituting it with 1 + 2x
Equation 2 becomes: 2(1 + 2x) - 3x = 5
2 + 4x - 3x = 5
2 + x = 5
x = 3
Substituting x = 3 into Equation 1 gives us y - 6 = 1, so y = 7.

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