 # 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:

• First ensure the equations are "lined up" underneath each other in the same format (the x-terms, y-terms, equals signs and constants underneath each other in order).
• Multiply the equations by appropriate numbers to make either the x terms or the y terms equal.
• By adding or subtracting the entire equations, you will cancel one of the variables.
• Solve this equation to for the one remaining variable.
• Use either of the original equations to find the solution of the other variable.

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 2x = 3 x = 1.5

So the solution to the simultaneous equations is:
 x = 1.5y = -2.5