Question

Solve the system of equations using substitution or elimination. Show all work for credit.

Answer 1

Using substitution:
first you have to express one variable in terms of the other, in this we can express y in terms of x:
$y = \frac{ - \frac{1}{2} x + 2}{3} \\ y = - x + 9$

Since both expressions are equal to y, you have to equal both expressions like this:
$\frac{ - \frac{ 1}{2}x + 2 }{3} = - x + 9$
Now you can solve the equation:
$- \frac{1}{2} x + 2 = 3( - x + 9) \\ - \frac{ 1}{2}x + 2 = - 3x + 27 \\ \\ - \frac{1}{2} x + 3x = 27 - 2 \\ \frac{5}{2} x = 25 \\ x = \frac{(25)(2)}{5} \\ x = 10$
Knowing x=10, you can use any of the expressions we found before to find y. In this case I'm going to use y= -x+9 because it's simpler but boy should give you the same result

$y = - (10) + 9 \\ y = - 1$
So, the answer is x=10 and y=-1