Question

Find the values of x and y for
$x+\frac{1}{2}y=\frac{9}{2}$
$\frac{1}{4}x-\frac{1}{6}y=\frac{5}{6}$

• A. x = 5, y = -1
• B. x = -4, y = 2
• C. x = 4, y = 1
• D. x = $\frac{1}{2}$, y = $-\frac{1}{3}$

Answer 1

The correct option is C

x = 4, y = 1

$x+\frac{1}{2}y=\frac{9}{2}$ __________(1)
$\frac{1}{4}x-\frac{1}{6}y=\frac{5}{6}$___(2)
From equation (1), we get
$x=\frac{9}{2}-\frac{1}{2}y$ ___________(3)
Plug this value of x in equation (2)
$\frac{1}{4}(\frac{9}{2}-\frac{1}{2}y)-\frac{1}{6}y=\frac{5}{6}$
$\frac{9}{8}-\frac{1}{8}y-\frac{1}{6}y=\frac{5}{6}$
$-\frac{7}{24}y=-\frac{7}{24}$
$y=1$
Substituting this value of y in equation (3), we get
$x=\frac{9}{2}-\frac{1}{2}$
$x=4$