# How do you solve the simultaneous equations  5c + 4d = 23 and 3c - 5d = -1?

Apr 18, 2018

Solution : $c = 3 , d = 2$

#### Explanation:

$5 c + 4 d = 23 \left(1\right) , 3 c - 5 d = - 1 \left(2\right)$ Multiplying equation (1) by

$3$ and equation (2) by $5$ we get,

$15 c + 12 d = 69 \left(3\right) , 15 c - 25 d = - 5 \left(4\right)$ Subtracting equation

(4) from equation (3) we get, $37 d = 74 \therefore d = \frac{74}{37} = 2$

Putting $d = 2$ in equation (1) we get, $5 c + 4 \cdot 2 = 23$ or

$5 c = 23 - 8 \mathmr{and} 5 c = 15 \mathmr{and} c = \frac{15}{5} = 3$

Solution : $c = 3 , d = 2$ [Ans]