SOLUTION: I have tried to solve this equation and cannot seem to get it right. Any help will be greatly appreciated. Solve the equations by substitution. If the equations are inconsistent

Algebra ->  Linear-equations -> SOLUTION: I have tried to solve this equation and cannot seem to get it right. Any help will be greatly appreciated. Solve the equations by substitution. If the equations are inconsistent      Log On


   

Question 561199: I have tried to solve this equation and cannot seem to get it right. Any help will be greatly appreciated.
Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution".
7x - 2 = 2y
3x = 2y - 1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +7x+-+2+=+2y+
(2) +3x+=+2y+-+1+
----------------
(2) +2y+=+3x+%2B+1+
Substitute this value of +2y+ into (1)
(1) +7x+-+2+=+3x+%2B+1+
Subtract +3x+ from both sides
(1) +4x+=+3+
(1) +x+=+3%2F4+
and, since
(2) +2y+=+3x+%2B+1+
(2) +2y+=+3%2A%283%2F4%29+%2B+1+
Multiply both sides by +4+
(2) +8y+=+9+%2B+4+
(2) +8y+=+13+
(2) +y+=+13%2F8+
The solution is (3/4, 13/8)
check answers:
(1) +7x+-+2+=+2y+
(1) +7%2A%283%2F4%29+-+2+=+2%2A%2813%2F8%29+
(1) +21%2F4+-+8%2F4+=+13%2F4+ ( I made 2 = 8/4 )
(1) +21%2F4+=+8%2F4+%2B+13%2F4+
(1) +21%2F4+=+21%2F4+
OK
(2) +3x+=+2y+-+1+
(2) +3%2A%283%2F4%29+=+2%2A%2813%2F8%29+-+1+
(2) +9%2F4+=+13%2F4+-+4%2F4+
(2) +9%2F4+=+9%2F4+
OK