Question

In the system of equations $5x-7y=-13$ and $2x+3y=13$, the values of x and y will be

• A. $\frac{52}{29}$ and $\frac{91}{29}$
• B. $\frac{31}{27}$ and $\frac{64}{27}$
• C. $\frac{51}{29}$ and $\frac{87}{29}$
• D. $\frac{52}{17}$ and $\frac{91}{17}$

Answer 1

The correct option is A $\frac{52}{29}$ and $\frac{91}{29}$

$\because 5x-7y=-13$............. (i)

$2x+3y=13$ ........... (ii)

On multiplying equation (i) by 2 and equation(ii) by 5 and then subtracting the equation (ii) from equation (i),

$10x-14y-(10x+15y)=-26-65$

or $10x-14y-10x-15y=-91$

or $-29y=-91\Rightarrow y=\frac{91}{29}$

On substituting this value of y in equation (i),

$5x-\frac{7\times 91}{29}=-13$

$\Rightarrow 5x=\frac{7\times 91}{29}-13$

$\Rightarrow 5x=\frac{637-377}{29}=\frac{260}{29}$

or, $x=\frac{260}{29\times 5}=\frac{52}{29}$

$\therefore x=\frac{52}{29},y=\frac{91}{29}$