Question

Solve: $x+4y=14$ and $7x-3y=5$

• A. $x=2,y=3$
• B. $x=5,y=3$
• C. $x=6,y=-4$
• D. $x=-3,y=7$

Answer 1

The correct option is A $x=2,y=3$

Given equations are

$x+4y=14$ ....(1)

and $7x-3y=5$ ....(2)

Let us slove equation (2) as

$7x=5+3y\Rightarrow x=\frac{5+3y}{7}$ ....(3)

Put this value in equation (1), we get

$\frac{5+3y}{7}+4y=14$

$\Rightarrow 5+3y+28y=98$

$\Rightarrow 31y=93$

$\Rightarrow y=3$

Substitute this value of $y$ in equation (3),

$x=\frac{5+3\left(3\right)}{7}$

$\Rightarrow x=\frac{14}{7}$

$\Rightarrow x=2$

Therefore, the solution is $x=2,y=3$.