Question

Find the value of x and y using substitution method:
$5x-6y=2$ and $6x-5y=9$

• A. $4$ and $-3$
• B. $-3$ and $-4$
• C. $-4$ and $-3$
• D. $4$ and $3$

Answer 1

Answer: (D)

$4$ and $3$

$5x-6y=2$ ------- $\left(1\right)$
$6x-5y=9$ ------- $\left(2\right)$

From equation $\left(1\right)$:

$\Rightarrow 6y=5x-2$

$\Rightarrow y=\frac{5x-2}{6}$

Substitute the value of $y$ in equation $\left(2\right)$ :

$\Rightarrow 6x-5y=9$

$\Rightarrow 6x-5\left(\frac{5x-2}{6}\right)=9$

$\Rightarrow 36x-25x+10=54$

$\Rightarrow 11x=54-10$

$\Rightarrow x=\frac{44}{11}=4$

Now, Substitute $x=4$ in equation $\left(1\right)$

$\Rightarrow 5x-6y=2$

$\Rightarrow 5\left(4\right)-6y=2$

$\Rightarrow 20-2=6y$

$\Rightarrow 18=6y$

$\Rightarrow y=\frac{18}{6}=3$

$\therefore$ the solution is $x=4$ and $y=3$