Simultaneous Equations

  • From: Dominic Walsh
  • Date: 2 September 1999
  • Subject: Simultaneous Equations

Can you give me some guidance how to solve the simultaneous equations:
     2x - 6y = 18   and
     3x + 5y = -8
using a method of elimination.

Maths Help suggests:

The method of elimination method works as follows:


The two equations you want to solve are already "lined up" properly.

Let us choose to make the coefficients of x the same:

First equation ×3: 6x-18y=54
Second equation ×2: 6x+10y=-16
Now subtract these two equations: -28y=70
Divide both sides by -28: y=-2.5


Now use your value for y in the first original equation to find x:

2x - 6y=18
2x - 6(-2.5)=18
2x + 15=18


So the solution to the simultaneous equations is:

x = 1.5
y = -2.5

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