Solve for x and y:
2x - y + 3 = 0, 3x - 7y + 10 = 0.
Rearranging the equations, we have
2x – y = - 3 …eq.1
3x – 7y = - 10 …eq.2
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply eq.1 by 7, so that variable y in both the equations have same coefficient.
Recalling equations 1 & 2,
2x – y = - 3 [×7
3x – 7y = - 10
⇒ 14x – 7y = - 21
3x – 7y = - 10
On solving the above two equations we get,
⇒ 11x = - 11
⇒ x = - 1
Substitute x = - 1 in eq.1/eq.2, as per convenience of solving.
Thus, substituting in eq.1, we get
2( - 1) – y = - 3
⇒ - 2 – y = - 3
⇒ y = - 2 + 3
⇒ y = 1
Hence, we have x = - 1 and y = 1.