Question

Solve the following pair of equations:

$3x-y=23$
$\frac{x}{3}+\frac{y}{4}=4$

• A. $x=-4;y=1$
• B. $x=-1;y=7$
• C. $x=9;y=4$
• D. $x=7;y=13$

Answer 1

The correct option is C $x=9;y=4$

We pick either of the equations and write one variable in terms of the other.

Let us consider the equation $3x-y=23$ and write it as

$y=3x-\mathrm{23...........}\left(1\right)$

Substitute the value of $y$ in Equation $\frac{x}{3}+\frac{y}{4}=4$ or $4x+3y=48$. We get

$4x+3(3x-23)=48$

i.e. $4x+9x-69=48$

i.e. $13x=117$

i.e. $x=9$

Therefore, $x=-9$

Substituting this value of $x$ in equation 1, we get

$y=27-23$

i.e. $y=4$

Hence, the solution is $x=9,y=4$.