# How do solve the following linear system?:  2x - 4y =3, 3x-5y=61 ?

Apr 9, 2018

Solution: $x = 114.5 , y = 56.5$

#### Explanation:

$2 x - 4 y = 3 \left(1\right) , 3 x - 5 y = 61 \left(2\right)$ Multiplied equation (1) by $3$

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

$6 x - 12 y = 9 \left(3\right) , 6 x - 10 y = 122 \left(4\right)$ , sbtracting equation (3)

from equation (4) we get, $2 y = 113 \therefore y = 56.5$. Substituting

$y = 56.5$ in equation (1) we get, $2 x - 4 \cdot 56.5 = 3$ or

$2 x - 226 = 3 \mathmr{and} 2 x = 229 \mathmr{and} x = 114.5$

Solution: $x = 114.5 , y = 56.5$ [Ans]