Question

solve the system by the elimination method
5x+3y=-7
7x-2y=17

Answer 1

We need to get rid of one of the variables. Since the y's have both a + and a -, let's get rid of them.

Multiply the top equation by 2 and the bottom equation by 3

10x + 6y = -14
21x - 6y = 51

Now add the two equations, notice the y's drop out

31x = 37

divide by 31

x = 37/31

Now to find y, chose one of the two original equations

I'll use the first one, it doesn't matter because this is not a "nice" answer.

5(37/31) + 3y = -7

185/31 + 3y = -7

subtract 185/31 from both sides

3y = -7 - 185/31 (We need common denominators)

3y = -217/31 - 185/31

3y = -402/31

divide by 3 (or multiply by 1/3)

y = -134/31

So the point of intersection is (37/31 , -134/31)

We should check in the other equation but since these numbers are so miserable, I used a calculator (using matrices, but that is for another time)

Hope it helps.

Answer 2

5x+3y=-7 mult this by 2
7x-2y=17 mult this by 3 gives

10x+6y=-14
21x-6y=51 add them we get
------------
31x +0 =37

x= 37/31 ans subs this to the ist eq, 5x+3y=-7

5(37/31)+3y=-7
165/31 +3y=-7
3y= -7 - 165/31
y=402/(31x3) =-134/31 ans

(37/31, -134/31) ans