How do you solve the following system: 5x+y=−7,12x−9y=−3?

1 Answer
Andrew I.
Feb 7, 2016

x=−2219, y=−2319.

Explanation:

I would recommend the method of elimination.

We have our 2 equations:

5x+y=−7
12x−9y=−3

Take the first equation and multiply it through by 9 to obtain, this will allow us to get the same number of ys on both equations so we can add them and eliminate as follows

45x+9y=−63

We can now add this to the second equation and we get:

(12x−9y)+(45x+9y)=(−3)+(−63)

Now, by gathering the like terms we see that y cancels to 0.

57x=−66→x=−6657=−2219

Now that we have a value for x put this value into back into either of the first or second equation and solve for y. Here we will use the first equation and get:

5(−2219)+y=−7
→y=5(2219)−7=11019−13319=−2319

And so we see that:

x=−2219, y=−2319.

As we chose the first equation to put our value of x into it is good practice to check these to make sure that the second equation is satisfied as well.

12(−2219)−9(−2319)=−26419+20719=−5719=−3

So the second equation is also satisfied.

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