Question

If $\frac{7}{2}x+\frac{5}{2}y$ $=5$ ; $4x+2y=7$, then what is the value of $x-y?$

• A. $1$
• B. $4$
• C. $2$
• D. $-2$

Answer 1

Answer: (B)

$4$

Given equations as :
$\frac{7}{2}x+\frac{5}{2}y=5...\left(1\right)$
$4x+2y=7...\left(2\right)$
From equation $\left(1\right)$ we have value of $y$:
$\Rightarrow 7x+5y=10$
$\Rightarrow 5y=10-7x$
$\Rightarrow y=\frac{10-7x}{5}$
Substitute value of $y$ in second equation will have $x$ value:
$4x+2\left(\frac{10-7x}{5}\right)=7$
$\Rightarrow 20x+2(10-7x)=35$
$\Rightarrow 20x+20-14x=35$
$\Rightarrow 6x=15$
$\Rightarrow x=\frac{5}{2}$
Now replacing $x$ value in equation 2nd will get $y$ value
$4\left(\frac{5}{2}\right)+2y=7$
$\Rightarrow 20+4y=14$
$\Rightarrow 4y=14-20$
$\Rightarrow 4y=-6$
$\Rightarrow 4y=-6$
$\Rightarrow y=\frac{-6}{4}$
$y=\frac{-3}{2}$
Now $x-y=\frac{5}{2}-\left(\frac{-3}{2}\right)$
$=\frac{5}{2}+\frac{3}{2}$
$=\frac{8}{2}$
$=4$
Hence, option $B$ is correct.