Question

Equation 1:

$x$	$-2$	$0$	$2$	$4$
$y$	$6$	$4$	$2$	$0$

Equation 2:

$x$	$-8$	$-4$	$0$	$4$
$y$	$-8$	$-7$	$-6$	$-5$

The linear equations represented by the data shown in the above tables form a system, what is the $x-$ coordinate of the solution to that system?

• A. $4$
• B. $8$
• C. $0$
• D. $-6$

Answer 1

Answer: (B)

$8$

The straight line in the first case passes through $(4,0)$ and $(0,4)$.

Hence its equation (by application of intercept form) will be $x+y=4$...(i)

The straight line in the second case passes through $(0,-6)$ and $(-8,-8)$.

Hence, its equation is given by $\frac{y+8}{x+8}=\frac{y+6}{x}$

$\Rightarrow 8x=6x+8y+48$

$\Rightarrow 2x=8y+48$

$\Rightarrow x-4y=24$....(ii)

Solving equation (i) and (ii) gives us the intersection point as $x=8$ and $y=-4$.