Let 1x+y=u and 1x−y=v. Then, the given system of equations becomes
5u−2v=−1 .(i)
15u+7v=10 .(ii)
Multiplying equation (i) by 3, this system of equations becomes
15u−6v=−3 .(iii)
15u+7v=10 .(iv)
Subtracting equation (iv) from equation (iii), we get
−13v=−13⇒v=1
Putting v=1 in equation (i), we get
5u−2=−1⇒u=15
Now, u=15⇒1x+y=15⇒x+y=5 ..(v)
and, v=1⇒1x−y=1⇒x−y=1 ..(vi)
Adding equations (vi) and (v), we get 2x=6⇒x=3.
Putting x=3 in equation (v), we get y=2.
Hence, x=3,y=2 is the solution of the given system of equations.