Question

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

3y=-1/2x+2
y=-x+9

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 = ( - (1)/(2) x + 2)/(3) \\ y = - x + 9`

Since both expressions are equal to y, you have to equal both expressions like this:

`( - ( 1)/(2)x + 2 )/(3) = - x + 9`
Now you can solve the equation:

`- (1)/(2) x + 2 = 3( - x + 9) \\ - ( 1)/(2)x + 2 = - 3x + 27 \\ \\ - (1)/(2) x + 3x = 27 - 2 \\ (5)/(2) x = 25 \\ x = ((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