Question

Write four solutions for each of the following equations:
(i) $2x+y=7$
(ii) $\pi x+y=9$
(iii) $x=4y$

Answer 1

(i) $2x+y=7$

$y=7–2x$

When $x=0$, then

$y=7–2\times 0$

$y=7–0$

$y=7$

When $x=1$ then

$y=7–2\times 1$

$y=7–2$

$y=5$

When $x=2$ then

$y=7–2\times 2$

$y=7-4$

$y=3$

When $x=3$ then

$y=7-2\times 3$

$y=7-6$

$y=1$

Hence, four solutions for equation $2x+y=7$ are $(0,7),(1,5),(2,3),(3,1)$.

(ii) $\pi x+y=9$

$y=9-\pi x$

When $x=-1$ then

$y=9-\pi \times -1$

$y=9+\pi$

When $x=0$ then

$y=9-\pi \times 0$

$y=9$

When $x=1$ then

$y=9-\pi \times 1$

$y=9-\pi$

When $x=2$ then

$y=9-\pi \times 2$

$y=9-2\pi$

Hence, four solution for equation $\pi x+y=9$ are $(-1,9+\pi ),(0,9),(1,9-\pi ),(2,9-2\pi )$.

(iii) $x=4y$

When $y=0$, then

$x=4\times 0$

$x=0$

When $y=1$ then

$x=4\times 1$

$x=4$

When $y=-1$ then

$x=4\times -1$

$x=-4$

When $y=2$ then

$x=4\times 2$

$x=8$

Hence, four solutions for equation $x=4y$ are $(0,0),(4,1),(-4,-1),(8,2).$

The provided answer is one of the various possible solutions. This question might have other solution too.