how do you solve x+y=-6 x-y=6 by elimination

Question

I tried and have been getting some weird answers that i don't think are right and my teacher has been away for awhile so the sub hasn't really helped with this much.

Answer 1

Let's see if we can solve this bad boy, Caitlin.

 

We have

 

x + y = -6

x - y = 6

 

If we add these two together we get

 

2x = 0

 

x = 0

 

Substituting the value 0 for x into either of the original expressions gives:

 

y = -6

 

so the point (0, -6) is the only one at which the two lines intersect.

 

What we have are two lines, one with slope 1 and the other with slope -1, but both of which have the y-intercept -6.

 

In general, Caitlin, if you find yourself having trouble with these sorts of problems, one of the easiest things you can do is the graph the equations on the same pair of coordinate axes.

 

Graphs never lie!

Answer 2

Hi Caitlin;

I would like to add to William's answer.

He initially adds the two equations together, then he plugs-in the result of x=0 to find the value of y.

Instead of plugging-in, what you can do is subtract the two equations from each other to establish y...

x+y=-6

-(x-y=6)

0+2y=-12

2y=12

y=-6