How do you solve the system 3x + 4y =2 and 2x + 3y =1?

Jul 30, 2018

color(green)(x = 2, y = -1

Explanation:

$3 x + 4 y = 2$, Eqn (1)

$2 x + 3 y = 1$, Eqn (2)

$6 x + 8 y = 4 , E q n \left(1\right) \cdot 2$

$6 x + 9 y = 3 , E q n \left(2\right) \cdot 3$

Subtracting one from the other,

$6 x + 8 y - 6 x - 9 y = 4 - 3$

$- y = 1$ or $y = - 1$

Substituting value of y in Eqn (1),

$3 x + 4 \cdot - 1 = 2$

$3 x - 4 = 2$

$3 x = 4 + 2 = 6$

$x = \frac{6}{3} = 2$