Question

Find the value of $p$ and $q$ using elimination method:
$3p+4q=-1$ and $6p-2q=8$

• A. $p=1$ and $q=1$
• B. $p=1$ and $q=-1$
• C. $p=-1$ and $q=1$
• D. $p=-1$ and $q=-1$

Answer 1

Answer: (B)

$p=1$ and $q=-1$

$3p+4q=-1$ .....(1)
$6p-2q=8$ ....(2)
Multiply equation (2) by $2$ and then add the equations
$3p+4q=-1$ ....(3)
$12p-4q=16$ .....(4)
_____________
$15p=15$
$\Rightarrow p=\frac{15}{15}$
$\Rightarrow p=1$
Put the value of $p=1$ in equation (1), we get
$3p+4q=-1$
$\Rightarrow 3\left(1\right)+4q=-1$
$\Rightarrow 4q=-1-3$
$\Rightarrow 4q=-4$
$\Rightarrow q=\frac{-4}{4}$
$\Rightarrow q=-1$
Therefore, the solution is $(1,-1)$.