Algebra 6th ed. p. 31

[Ceej05]

Solve for x and y:
y= 2x + 9
7x + 3y = -51

I tried to make it so that I could isolate X and thus multiplied the first equation by -3 and moved over the 2x to get -2x + y = 9
In adding together the equations, I got
7x + 3y = -51
+6x - 3y = -27

Then 13x = -78 and x = -78/13
Plugging that in to one of the original equations, I then got
y = (-52/13)+9

Where did I go wrong?

[RonPurewal]

x = -78/13
Plugging that in to one of the original equations, I then got
y = (-52/13)+9

presumably you're plugging into the equation y = 2x + 9.

if that's the equation, then you are somehow multiplying 2 by -78/13 and coming up with -52/13. that's not right.

[RonPurewal]

by the way, did you notice that "-78/13" is just -6?

even if you didn't notice that, plugging in gives
y = 2(-78/13) + 9
y = -156/13 + 117/13
y = -39/13
... and you're definitely going to notice that this is just y = -3. if y is such a "nice" number, then x will be pretty nice too.