Substitution/Elimination Form

Question

Substitution Form:

2x-3y=2 x+y=-1

x+y=-1

 

Elimination From: 

2x/3 - 4y/5 = 1 and 3x-y=-7

Answer 1

2x-3y=2

x+y = -1    Solve this equation for x by subtracting y.

    x = -1 - y     Substitute this equation into the first equation.

2(-1 - y) - 3y = 2

-2 - 2y - 3y = 2   Collect like terms and add 2 to both sides.

             -5y = 4   Divide both sides by -5.

                 y = - 4/5   Substitute this into the second equation.

x - 4/5 = -1     Add 4/5 to both sides.

          x = -1/5        (-1/5, -4/5)

2nd Problem:

15(2x/3 - 4y/5) = 15(1)

10x - 12y = 15  (Eq. 1)

(-12)(3x-y) = (-12)(-7)

-36x + 12y = 84    (Eq. 2)   Add Eq. 1 and Eq. 2

   10x - 12y = 15

           -26x = 99  Divide both sides by -26.

                 x =-99/26   Substitute into 3x-y=-7

3(-99/26) - y = -7

-297/26 - y = -7      -7 = -182/26   (need common denominators)

-y = -182/26 + 297/26

-y = 115/26

y = -115/26     (-99/26, -115/26)

I sure hope you're in a very accelerated algebra class, Alina, because this is an "awful" problem for a first year algebra class.