SOLUTION: 8x+5y=177.50 12x+6y=255.00 I need help solving this by either the substitution method or elimination method

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 8x+5y=177.50 12x+6y=255.00 I need help solving this by either the substitution method or elimination method      Log On


   

Question 1119843: 8x+5y=177.50
12x+6y=255.00

I need help solving this by either the substitution method or elimination method
Found 3 solutions by Alan3354, MathTherapy, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
8x+5y=177.50
12x+6y=255.00
-----------
8x+5y= 177.50
8x+4y= 170 --- times 2/3
================== Subtract

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

8x+5y=177.50
12x+6y=255.00

I need help solving this by either the substitution method or elimination method
8x + 5y = 177.5 ------ eq (i)

12x + 6y = 255_____3(4x + 2y) = 3(85)______4x + 2y = 85 ---- eq (ii)

- 8x - 4y = - 170 ------- Multiplying eq (ii) by - 2 ------- eq (iii)

highlight_green%28matrix%281%2C3%2C+y%2C+%22=%22%2C+7.5%29%29 ------- Adding eqs (iii) & (i)

4x + 2(7.5) = 85 ------- Substituting 7.5 for y in eq (ii)

4x + 15 = 85

4x = 70

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+70%2F4%2C+%22=%22%2C+17.5%29%29

You can do your own check!

Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


When the two equations are both in the form Ax+By=C, elimination is virtually always faster than substitution.

Multiply the first equation by 3 and the second by -2 and add; the x variable is eliminated.
   24x+15y =  532.50
  -24x-12y = -510
  ------------------
        3y = 22.50
         y = 7.5


Then substitute that value of y in either of the original equations to find x.

12x+6(7.5) = 255
12x+45 = 255
12x = 210
x = 210/12 = 17.5