Question

Solve each pair of equation by using the substitution method.
$2x+3y=9$
$3x+4y=5$

• A. $x=-21$ and $y=7$
• B. $x=1$ and $y=17$
• C. $x=-21$ and $y=17$
• D. None of these

Answer 1

Answer: (C)

$x=-21$ and $y=17$

$2x+3y=9---\left(i\right)$

$3x+4y=5--\left(ii\right)$

From equation $\left(i\right)$, we get

$\Rightarrow 2x=9-3y\Rightarrow x=\frac{9-3y}{2}---\left(iii\right)$

Substituting equation $\left(iii\right)$ in equartion $\left(ii\right)$, we get

$\Rightarrow 3\left(\frac{9-3y}{2}\right)+4y=5$

$\Rightarrow 27-9y+8y=10$

$\Rightarrow y=27-10=17$

$\therefore x=\frac{9-3\times 17}{2}=\frac{-42}{2}=-21$