x+y=-12,x-y=2

Question

should be solved with substitution method

Answer 1

Hi Ronak, here are the steps to solve the problem

x+y=-12    (1)

x-y=2        (2)

solve equ. (2) for x by adding y to both sides 

x=y+2     (3)

substitute equ.(3) in equ. (1)

(2+y)+y=-12

2+2y=-12

2y=-12-2     by subtracting 2 from both sides

2y=-14

y=-7  by dividing both sides by 2

substitute y=-7 in equ.(3)

x=-7+2

x=-5

then (-5,-7) are the values of (x,y)

Answer 2

Hello Ronak! The substitution method is definitely correct, but you can get the same solution a bit faster by using what's called linear combination...so basically set it up like an addition problem with one equation on top and the other on the bottom and add down. 
 
x    + y   = -12
x    -  y   =  2
2x +0y = -10
        2x = -10
          2       2
          x = -5

So, to put the above work in words, I started off by combining the x terms...x + x = 2x. Then I look at the y's and we have a "+y+ and a "-y" which means they cancel out to zero. The constant terms on the right side of the equation make -12 + 2, which is -10. Now we have it simplified to 2x = -10....divide both sides by 2 to isolate "x", and we get x = -5. Now that we have the x-value, all we do is plug it into either of the 2 original equations and solve for the y-value as so:

  x   + y = -12 
(-5) + y = -12
 + 5           + 5
          y = -12 + 5
          y = - 7

So to put that in words, we picked one equation (I picked the first one), then we plug in the value we got for x, which was -5. Then, to isolate y, we added the 5 to both sides, then we solved for y = -12 + 5, leaving us with y = -7.

Final answer: (x = -5, y = -7)

This shortcut can be used any time you see a term that can be cancelled, like in this example we had the +y and -y  leaving us with only x terms when we do a linear combination. I hope this helps. :)

Answer 3

You can approach this from a few different ways. I would set the second equation to be: x=y+2

Then, take the above equation and plug it into the x variable in the first equation. 

Now, the equation should be: y+2+y=-12. Simplifying, 2y=-14. 2 divided by -14 equals -7, so y=-7.

Plug -7 for y into the second equation: x-(-7)=2, so x+7=2. Subtracting 7 from both sides gives you x=-5.

Hope this helps!

 

Answer 4

Hi Ronak, You can solve for x from one of the equations and plug this value into the other equation. For example, you can solve for x from the first equation and get x=-12-y. Then replace the x from the other equation by this value (-12-y) Like this: x-y=2 (-12-y)-y=2 ;I just changed the x with -12-y Now that you have only one variable, you can solve for it. -12-2y=2 Add 12 both sides -2y=14 divide by -2 y=-7 You've solved for y! You can plug this y into any of the two equations to solve for x. You should be getting x=-5. Good luck!