Question

How do you solve the following system?: `x - 3y = 0 , -3x + 7y = 1`

Answer 1

`x = -1 1/2 , and y = (-1)/2`

Explanation:

In order to work with these simultaneous equations, I will make the coefficients of the x terms both 3. But it will be easier to have them as additive inverses, (because by adding: -3 +3 = 0)

`" "x - 3y = 0 " A"`
`" "-3x + 7y = 1 " B"`

A x 3: `" "3x - 9y = 0" "C`

B+C: `" " -2y = 1 " the x-terms have been eliminated"`
`" " y = -1/2`

If `y = -1/2, " subst in A to find x"`

`x - 3((-1)/2) = 0`

`x + 3/2 = 0`

`x = -3/2`