<span>6x + 7y = 11 . . . . (1)
5x + 2y = 13 . . . . (2)
</span><span>
6x + 7y = 11 (multiply through by 2) </span>→ 12x + 14y = 22 (
)
<span>
5x + 2y = 13 (multiply through by 7) </span>→ 35x + 14y = 91 (
)
by subtracting () from ()
⇒ (35x + 14y) - (12x + 14y) = 91 - 22
⇒ 35x - 12x + 14y - 14y = 91 - 22
⇒ 23x = 69
⇒ 23x ÷ 23 = 69 ÷ 23
∴ x = 3
By substituting found value of x into (2),
⇒ 5(3) + 2y = 13
⇒ 15 + 2y = 13
⇒ 2y = 13 - 15
2y = -2
∴ y = -1
Thus the solution to the system is (3 , -1)
5x + 2y = 13 . . . . (2)
</span><span>
6x + 7y = 11 (multiply through by 2) </span>→ 12x + 14y = 22 (
<span>
5x + 2y = 13 (multiply through by 7) </span>→ 35x + 14y = 91 (
by subtracting (
⇒ (35x + 14y) - (12x + 14y) = 91 - 22
⇒ 35x - 12x + 14y - 14y = 91 - 22
⇒ 23x = 69
⇒ 23x ÷ 23 = 69 ÷ 23
∴ x = 3
By substituting found value of x into (2),
⇒ 5(3) + 2y = 13
⇒ 15 + 2y = 13
⇒ 2y = 13 - 15
2y = -2
∴ y = -1
Thus the solution to the system is (3 , -1)