Question

How do you solve the system of equations `-6x + y = 10` and `x + 5y = - 12` by elimination?

Answer 1

To do it by elimination means to eliminate one variable (either x or y)

Explanation:

If you label the equations (i) and (ii) it makes your job easier :

-6x + y = 10 (i)
x + 5y = -12 (ii)

Decide which you think will be simpler to eliminate by adding or subtracting (it doesn't matter, just one is generally a bit easier than the other.) I'm going to eliminate y. I do this by making the multiplier for y the same in two equations, but it has the opposite sign (+3y and -3y for example.)

equation (i) multiplied by -5 gives:
30x - 5y = -50 (iii)

Adding equations (ii) and (iii) gives:
31x +5y -5y = -62 and the y factor has been eliminated from the equation.

so x = -62/31 = -2 (iv)

I now resubstitute this value for x into equation (i) or (ii). I'll choose equation (ii)

-2 + 5y = -12 (v)

so 5y = -10 = -2

This is an unusual answer ... the values for x and y are normally different, but i don't see an error yet!