how to solve this problem step by step

Question

3x+2y=-8

-9x-4y=-2

Answer 1

1) For getting y, make x disappear:

 

3x+2y=-8   ...... equation A
-9x-4y=-2   ...... equation B

 

Multiply both left and right sides of equation A by 3 , then we get equation A' and B:

 

 9x+6y=-24 ...... equation A'
-9x- 4y=-2   ...... equation B

 

Then add left sides of the two equations and add right sides of the two equations, the 9x-9x will make x disappear, then we get:

 

        2y =-26

     So y = -13.

 

2) We can put the value of y back to either equation A or equation B to get the value of x:

 

For example, using equation A:

      3x+2y=-8

 

So 3x + 2*(-13)        = -8

     3x + (-26)           = -8

     3x      -26  + 26   = -8+26

     3x                       = 18

 

So  x = 6 

 

 

3) Now we can put x=6 and y=-13 into the equation B to make sure we did not make mistakes:

 

equation B:     -9x  - 4y=-2

the left side = -9*6 - 4*(-13) 

                  = -54 +52

                   = -2

                   = the right side

 

Which means we get the right answer as

 

x=6

y=-13

              

      

 

 

 

Answer 2

 The solution is as follows:

 

3x + 2y = -8

-9x - 4y = -2  first you need to form a 'method of attack' which is efficient for the given problem

                     I recommend to multiply each term in the first equation by 3 so that the x terms in both equations

                     cancel out

 

3(3x) + 3(2y) = 3(-8) leaves you with 9x + 6y = -24 ... then you just add the two equations

 

9x + 6y = -24

-9x - 4y = -2

____________

      2y = -26 Then divide both sides by 2

       2       2

____________

       y = -13

 

now that you know what y is, you can substitute -13 into either equation to solve for x:

 

9x + 6(-13) = -24 which gives you the equation:

9x - 78 = -24 then add 78 to each side

    + 78   +78

___________

9x        = 54

9              9   (divide both sides by 9)

___________

    x = 6

Therefore, the solution is y = - 13 and x = 6. Just to be sure, of course, it is always a good idea to plug 6 into one of the original equations to make sure.

9(6) + 6y = -24

54 + 6y = -24

-54          -54 (add -54 to both sides)

___________

         6y = -78

         6         6 (divide both sides by 6)

___________

           y = -13 There you have it! The answer checks out with both the x and y substitutions, so the solutions must be correct.

Will Grondski

Princeton, NJ 08543