Question

Solve graphically, the following pairs of equations:

$\frac{x+1}{4}=\frac{2}{3}(1-2y)$

$\frac{2+5y}{3}=\frac{x}{7}-2$

• A. $x=3,y=-1$
• B. $x=7,y=-1$
• C. $x=5,y=-1$
• D. $x=4,y=-1$

Answer 1

Answer: (B)

$x=7,y=-1$

$\frac{x+1}{4}=\frac{2}{3}(1-2y)$

$x+1=\frac{8}{3}(1-2y)$

$⟹x=\frac{8(1-2y)}{3}-1$

$⟹x=\frac{8(1-2y)-3}{3}$

$⟹x=\frac{8-16y-3}{3}$

$⟹x=\frac{5-16y}{3}$

Let, $y=2$, then $x=\frac{5-16\left(2\right)}{3}=-9$

Similarly, when $y=-1,x=7$

Now,

$\frac{2+5y}{3}=\frac{x}{7}-2$

$⟹\frac{2+5y}{3}+2=\frac{x}{7}$

$⟹\frac{2+5y+6}{3}=\frac{x}{7}$

$⟹\frac{7(8+5y)}{3}=x$

$⟹\frac{56+35y}{3}=x$

Let, $y=-1$, then $x=\frac{56+35(-1)}{3}=7$

Similarly, when $y=-2,x=-8$

$\therefore$ the intersecting point is $(7,-1)$