Question

Solve $2x-y=12$ and $x+3y+1=0$ and hence find the value of m for which y = mx + 3

• A. $x=1,y=9,m=23$
• B. $x=5,y=-2,m=-1$
• C. $x=2,y=-1,m=-8$
• D. None of these

Answer 1

The correct option is B $x=5,y=-2,m=-1$

The equations are
$\Rightarrow 2x-y=\mathrm{12.....}eq\left(1\right)$
$\Rightarrow x=\frac{12+y}{2}$
$\Rightarrow x+3y=-\mathrm{1.....}eq\left(2\right)$
put the value of x in eq (2 )
$\Rightarrow \frac{12+y}{2}+3y=-1$
$\Rightarrow 12+y+6y=-2\Rightarrow 7y=-14\Rightarrow y=-2$
put the value of y in eq ( 1 )
$\Rightarrow 2x-(-2)=12\Rightarrow 2x=10\Rightarrow x=5$
$Nowy=mx+\mathrm{3....}eq\left(3\right)$
put x=5 and y=-2 in eq ( 3 )
$\Rightarrow -2=m\times 5+3\Rightarrow -5m=5\Rightarrow m=-1$
$\Rightarrow x=5,y=-2,m=-1$