# How do you solve the following system?: 8x -5y =9 , 5x -7y = 2

Mar 23, 2018

Solution: $x = \frac{53}{31} , y = \frac{29}{31}$

#### Explanation:

8x-5y=9 ; (1) ; 5x-7y=2 ; (2) . Multiplying equation(1)

by $5$ and equation(2) by $8$ we get,

40x-25y=45 ; (3) ; 40x-56y=16 ; (4) Subtracting

equation(4) from equation(3) we get,

$31 y = 29 \therefore y = \frac{29}{31}$ Putting $y = \frac{29}{31}$ in equation (1)

we get $8 x - 5 \cdot \frac{29}{31} = 9 \mathmr{and} 8 x = 9 + \frac{145}{31} \mathmr{and} 8 x = \frac{424}{31}$ or

$x = \frac{424}{31 \cdot 8} = \frac{53}{31} \therefore$ Solution:$x = \frac{53}{31} , y = \frac{29}{31}$ [Ans]