# How do you solve the system of equations algebraically -3x+10y=5, 2x+7y=24?

Aug 26, 2017

Solution: $x = 5 , y = 2$

#### Explanation:

$- 3 x + 10 y = 5 \left(1\right) ,$ 2x+7y = 24 (2) 

Multiplying equation (1) by $2$ and equation (2) by $3$

we get , $- 6 x + 20 y = 10 \left(3\right) ,$ 6x+21y = 72 (4)

Adding equation (3) and equation (4) we get,

$41 y = 82 \mathmr{and} y = \frac{82}{41} - 2$ . Putting $y = 2$ in equation (1) we get,

$- 3 x + 10 \cdot 2 = 5 \mathmr{and} - 3 x + 20 = 5 \mathmr{and} 3 x = 20 - 5$ or

$3 x = 15 \mathmr{and} x = \frac{15}{3} = 5$

Solution: $x = 5 , y = 2$ [Ans]