How do you solve 2p+5q=9, 3p-2q=4?

Apr 8, 2018

$p = \frac{38}{19}$ and $q = 1$

Explanation:

2p + 5q = 9 color(white)(..) ……(1)
3p - 2q = 4 color(white)(..) ……(2)

Multiply equation $\left(1\right)$ by $2$ and equation $\left(2\right)$ by $5$

$4 p + 10 q = 18$
$15 p - 10 q = 20$

$4 p + 10 q + 15 p - 10 q = 18 + 20$

$19 p = 38$

$\textcolor{b l u e}{p = \frac{38}{19}}$

Substitute $p = \frac{38}{19}$ in equation $\left(1\right)$

$2 \left(\frac{38}{19}\right) + 5 q = 9$

$\frac{76}{19} + 5 q = 9$

$5 q = 9 - \frac{76}{19}$

5q = (9 × 19/19) - 76/19

$5 q = \frac{171}{19} - \frac{76}{19}$

$5 q = \frac{171 - 76}{19}$

$5 q = \frac{95}{19}$

q = 95/(19 × 5) = 95/95

$\textcolor{b l u e}{q = 1}$