Question

How do you solve this system of equations: `x- 5y = 6 and y = - \frac { 1} { 2} x - \frac { 1} { 2}`?

Answer 1

`x=1 and y =-1`

Explanation:

The second equation is not comfortable because of the fractions. Multiply through by `2` to cancel the denominators.

`ycolor(blue)(xx2) = -1/2xcolor(blue)(xx2)-1/2color(blue)(xx2)" "rarr 2y = -x-1`

Now we have `color(red)(x)-5y =6" "and" "2y=color(red)(-x)-1`

Make the `x` term the subject in each case:

`color(red)(x)= 5y+6" "and" "color(red)(x)=-2y-1`

We know that `color(red)(x) =color(red)(x)" "` so it follows that:

`5y+6 = -2y-1" "larr` now solve for `y`

`5y +2y = -1-6`

`7y = -7`

`y =-1`

`color(red)(x)= 5(-1)+6`

`x = -5+6`

`x=1`

Check using the other equation.

`color(red)(x)=-2y-1`

Is `1" "=" "-2(-1)-1`?

`1 =2-1`

`1=1`