Solve for x and y:
, 5x = 2y + 7
We have,
…eq.1
5x = 2y + 7 or 5x – 2y = 7 …eq.2
Let us first simplify eq.1 by taking LCM of denominator,
Eq.2 ⇒
⇒ 8x – 3y = 12 …eq.3
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply eq.2 by 3 and eq.3 by 2, so that variable y in both the equations have same coefficient.
Recalling equations 2 & 3,
5x – 2y = 7 [×3]
8x – 3y = 12 [×2]
⇒ 15x – 6y = 21
16x – 6y = 24
On solving the above equations we get,
- x – 0 = - 3
⇒ - x = - 3
⇒ x = 3
Substitute x = 3 in eq.2/eq.3, as per convenience of solving.
Thus, substituting in eq.2, we get
5(3) – 2y = 7
⇒ 15 – 2y = 7
⇒ 2y = 15 – 7
⇒ 2y = 8
⇒ y = 4
Hence, we have x = 3 and y = 4