SOLUTION: three times the sum of two numbers exceeds twice their difference by five, while half the sum is two more than the difference. what are the two numbers?

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Question 112964: three times the sum of two numbers exceeds twice their difference by five, while half the sum is two more than the difference. what are the two numbers?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be x and y
A) 3(x+y)=2(x-y)+5
B) (x+y)/2=x-y+2
.
A) 3x+3y=2x-2y+5
x+5y=5
B)x+y=2x-2y+4 multiply both sides by 2.
-x+3y=4
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+5%5Cy+=+5%2C%0D%0A++++-1%5Cx+%2B+3%5Cy+=+4+%29%0D%0A++We'll use substitution. After moving 5*y to the right, we get:
1%2Ax+=+5+-+5%2Ay, or x+=+5%2F1+-+5%2Ay%2F1. Substitute that
into another equation:
-1%2A%285%2F1+-+5%2Ay%2F1%29+%2B+3%5Cy+=+4 and simplify: So, we know that y=1.125. Since x+=+5%2F1+-+5%2Ay%2F1, x=-0.625.

Answer: system%28+x=-0.625%2C+y=1.125+%29.

Check:
A)
3(-.625+1.125)=1.5
2(-6.25+1.125)=-3.5 difference of 5
.
B)
(-.625+1.125)/2=.25
-.625-1.125=-1.75 difference of 2
.
Ed