Hi Ahmad;
3/4x+1/2y=15
1/2x+4/6y=13
I am assuming this is...
(3/4)x+(1/2)y=15
(1/2)x+(4/6)y=13
Let's begin with the first equation...
(3/4)x+(1/2)y=15
Fractions are so confusing. Let's note that the denominators (also known as divisors) are 4 and 2. Let's multiply everything by 4...
4[(3/4)x+(1/2)y]=4(15)
3x+2y=60
Let's proceed with the second equation...
(1/2)x+(4/6)y=13
Let's multiply both sides by 6...
6[(1/2)x+(4/6)y]=6(13)
3x+4y=78
3x+4y=78
3x+2y=60
Let's subtract the first equation from the second...
0+2y=18
2y=18
Let's divide both sides by 2...
(2y)/2=18/2
y=9
Original equations...
(3/4)x+(1/2)y=15
Let's plugin 9...
(3/4)x+(1/2)(9)=15
(3/4)x+4.5=15
Let's subtract 4.5 from both sides...
(3/4)x+4.54.5=154.5
(3/4)x=10.5
Let's multiply both sides by (4/3)...
(4/3)(3/4)x=10.5(4/3)
x=42/3=14
(1/2)x+(4/6)y=13
Let's plug in y=9 and x=14 to verify...
(1/2)(14)+(4/6)(9)=13
7+(36/6)=13
7+6=13
11/17/2013

Vivian L.