Question

Solve the equations using elimination method:
$24(x+y)=-18$ and $2x-y=1$

• A. $(\frac{1}{12},\frac{5}{6})$
• B. $(\frac{-1}{12},\frac{-5}{6})$
• C. $(\frac{1}{12},\frac{-5}{6})$
• D. $(\frac{-1}{12},\frac{5}{6})$

Answer 1

The correct option is C $(\frac{1}{12},\frac{-5}{6})$

First simplify the equations:
$24(x+y)=-18\Rightarrow 4x+4y=-3$ ----- (1)
$2x-y=1$ ----- (2)
Multiply equation (2) by 4 and then add the equations
$4x+4y=-3$ ----- (3)
$8x-4y=4$ ----- (4)
_____________
$12x=1$
$x=\frac{1}{12}$
Put the value of $x$ in equation (2), we get
$2x-y=1$
$2\left(\frac{1}{12}\right)-y=1$
$\frac{1}{6}-y=1$
$y=\frac{-5}{6}$
Therefore the solution is ($\frac{1}{12},\frac{-5}{6}$)