# How do you solve the system 3x/8-3y/5=33/80 and  4x/7+4y/5=37/35?

Jun 9, 2018

Solution: $x = - 24.38 , y = - 17.3$

#### Explanation:

$3 \frac{x}{8} - 3 \frac{y}{5} = \frac{33}{80} \mathmr{and} 3 + \frac{x}{8} - \left(3 + \frac{y}{5}\right) = \frac{33}{80}$ or

$\cancel{3} + \frac{x}{8} - \cancel{3} - \frac{y}{5} = \frac{33}{80}$ multiplying by $80$ on

both sides we get, $10 x - 16 y = 33 \left(1\right)$

$4 \frac{x}{7} + 4 \frac{y}{5} = \frac{37}{35} \mathmr{and} 4 + \frac{x}{7} + 4 + \frac{y}{5} = \frac{37}{35}$ or

$8 + \frac{x}{7} + \frac{y}{5} = \frac{37}{35}$ multiplying by $35$ on

both sides we get, $280 + 5 x + 7 y = 37 \mathmr{and} 5 x + 7 y = - 243 \left(2\right)$

Multiplying equation (2) by $2$ we get, $10 x + 14 y = - 486 \left(3\right)$

Subtracting equation (3) from equation (1) we get,

$- 16 y - 14 y = 33 - \left(- 486\right) \mathmr{and} - 30 y = 519 \mathmr{and} y = - 17.3$

Putting $y = - 17.3$ in equation (1) we get,

$10 x - 16 \cdot \left(- 17.3\right) = 33 \mathmr{and} 10 x + 276.8 = 33$ or

$10 x = 33 - 276.8 \mathmr{and} 10 x = - 243.8 \mathmr{and} x = - 24.38$

Solution: $x = - 24.38 , y = - 17.3$ [Ans]