Solve for x and y:
2x - 3y = 13, 7x - 2y = 20.
We have,
2x – 3y = 13 …eq.1
7x – 2y = 20 …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 2 and eq.2 by 3, so that variable y in both the equations have same coefficient.
Recalling equations 1 & 2,
2x – 3y = 13 [×2]
7x – 2y = 20 [×3]
⇒ 4x – 6y = 26
21x – 6y = 60
On solving the two equations we get,
- 17x = - 34
⇒ x = 2
Substitute x = 2 in eq.1/eq.2, as per convenience of solving.
Thus, substituting in eq.1, we get
2(2) – 3y = 13
⇒ - 3y = 13 – 4
⇒ - 3y = 9
⇒ y = - 3
Hence, we have x = 2 and y = - 3.