SOLUTION: I was hoping to find the answer to this problem as well as the work on how to solve it. It is a particularly important review question I want to have on hand to refer back to if I

Algebra ->  Linear-equations -> SOLUTION: I was hoping to find the answer to this problem as well as the work on how to solve it. It is a particularly important review question I want to have on hand to refer back to if I       Log On


   



Question 664543: I was hoping to find the answer to this problem as well as the work on how to solve it. It is a particularly important review question I want to have on hand to refer back to if I get another question like it in the future on homework etc. Thanks!
Solve the following system of equations for x and y:
1/2x + 3/2y = 3/8
9/x - 6/y = 15/12

Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following system of equations for x and y:
1/2x + 3/2y = 3/8
9/x - 6/y = 15/12
--------------------
1/2x + 3/2y = 3/8
Do you mean (1/2)x + (3/2)y? or 1/(2x) + 3/(2y) ?
I would assume the former, but the 2nd equations appears to have the variables in the denominator.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +1%2F%282x%29+%2B+3%2F%282y%29+=+3%2F8+
(2) +9%2Fx+-+6%2Fy+=+15%2F12+
--------------------------
Are these the right equations?
If so,
Multiply both sides of (1) by +8x%2Ay+
(1) +4y+%2B+12x+=+3x%2Ay+
Multiply both sides of (2) by +12x%2Ay+
(2) +108y+-+72x+=+15x%2Ay+
-------------------------
Multiply both sides of (1) by +6+
and add the equations
(1) +24y+%2B+72x+=+18x%2Ay+
(2) +108y+-+72x+=+15x%2Ay+
+132y+=+33x%2Ay+
Divide both sides by +y+
+x+=+132%2F33+
+x+=+44%2F11+
+x+=+4+
Now plug this back into (1) or (2)
(1) +4y+%2B+12x+=+3x%2Ay+
(1) +4y+%2B+12%2A4+=+3%2A4%2Ay+
(1) +4y+%2B+48+=+12y+
(1) +8y+=+48+
(1) +y+=+6+
------------
check solutions:
(1) +1%2F%282x%29+%2B+3%2F%282y%29+=+3%2F8+
(1) +1%2F%282%2A4%29+%2B+3%2F%282%2A6%29+=+3%2F8+
(1) +1%2F8+%2B+1%2F4+=+3%2F8+
(1) +3%2F8+=+3%2F8+
OK
and
(2) +9%2Fx+-+6%2Fy+=+15%2F12+
(2) +9%2F4+-+6%2F6+=+15%2F12+
(2) +27%2F12+-+12%2F12+=+15%2F12+
(2) +27+-+12+=+15+
(2) +15+=+15+
OK