the y-coordinate of the solution to the system shown is _____. 5x + y = 6 & 5x + 3y = -4

Question

Addition Method - Algebra I

Answer 1

Using the elimination method: 

      5x + y = 6

+  -5x + -3y = 4                  (multiplied everything in equation 2 by -1) 

     0x + -2y = 10                 (add equations together; the x terms cancel) 

     y = -5                             (solve for y) 

Answer 2

I also prefer to use the elimination method.  You can usually find your answer much quicker and are less likely to make mistake in your work.

Answer 3

This is how I particularly like to solve these problems.

5x + y =6

5x + 3y = -4

I would first solve for one of the variables either x or y. In this case I’m going to choose y.

5x + y =6

y= 6-5x

Then you plug that in for the second equation.

5x + 3 (6-5x) = -4

5x + (3*6) – (3*5x) = -4

5x + 18 – 15x = -4

5x -15x = -4 – 18

-10x = -22

10x = 22

x=22/10 = 2.2

Then you put that back into the first equation.

5(2.2) + y =6

11 + y = 6

y = 6-11

y= -5

So the answer to your question is y = -5.