# If 2x + 3y = 17 and 3x + 4y = 24, then what is 5x +7y?

May 9, 2018

color(indigo)(5x + 7y = (5 * 4) + (7 * 3) = 41

#### Explanation:

$2 x + 3 y = 17 , \text{ Eqn (1)}$

6x + 9y = 51, color(red)(" Eqn (3) = 3 * Eqn (1)"

$3 x + 4 y = 24 , \text{ Eqn (2)}$

6x + 8y = 48, color(red)(" Eqn (4) = 2 * Eqn (2)"

6x - 6x + 9y - 8y = 51 - 48, color(purple)(" Eqn (3) - Eqn (4)"

$y = 3$

Substituting value of y in eqn 91),

$2 x + 9 = 17$

$2 x = 8 , x = 4$

color(indigo)(5x + 7y = (5 * 4) + (7 * 3) = 41