System of eqns Substitution: -5x - 8y = 17, 2x - 7y = -17

[Panthera]

Please i need help, I understand how you are suppose to solve substitution until I hit a fraction term. Then I am miserably confused how to get rid of that fraction in the next equation....?This is very important to me that I learn & understand this, as it is necessary for me to get my pre-requist (CLEP) satisfied to be in to my Radiology course

Ex.I tried this equation & when I got to the substitution I got lost.

-5x- 8y =17
2x -7y=-17 I tried to solve for X : 2x=-17+7y
2x/2 =-17/2 +7y/2

-5x(-17/2 +7x/2)-8y =17
now in trying to solve for Y i got
85x/2-35x/2 -8y =17
50x/2 -8y =17 If both terms become X where is a constant # to move to the other side of
the equation to combine with 17? you can't combine a 50x with 17,they are not like terms. In dealing with fractions, I know i must have made a error in my computation some where, there had to be a constant term to combine with 17, but Im lost for understanding where I went wrong with this.

 

[Loren]

\(\displaystyle y=\frac{2x+6}{3}= \frac{x}{3}+1\)

\(\displaystyle -7x+8(\frac{x}{3}+1)=-5\)

\(\displaystyle -7x + \frac{8x}{3}+8=-5\)

\(\displaystyle 3(-7x + \frac{8x}{3}+8)=3(-5)\)

\(\displaystyle -21x + 8x +24 = -15\)

 

[Denis]

-2x+ 6y =6
-7x +8y=-5

Another way; re-write your equations:
2x = 6y - 6 ; x = 3y - 3 [1]
7x = 8y + 5 [2]

Substitute [1] in [2]:
7(3y - 3) = 8y + 5

Couple more steps and you're finished...