Question

Write four solutions for the given equation:

$3x+4y=7$

Answer 1

Finding four solution for equation :$3x+4y=7$

The given equation will be written as;

$3x+4y-7=0$$·····\left(i\right)$

Putting $y=1$in equation $\left(i\right)$

we get, $3x+4\left(1\right)-7=0$

$\Rightarrow x=\frac{3}{3}=1$

Thus, $\left(1,1\right)$ is a solution of equation $\left(i\right)$.

Putting $x=2$ in equation $\left(i\right)$,

$\Rightarrow 3\left(2\right)+4y-7=0$

$\Rightarrow 4y=7-6$

$\Rightarrow y=\frac{1}{4}$

Thus, $\left(2,\frac{1}{4}\right)$ is a solution of equation $\left(i\right)$.

Putting $x=-3$ in equation $\left(i\right)$

$\Rightarrow 3\left(-3\right)+4y-7=0$

$\Rightarrow 4y=7+9$

$\Rightarrow y=\frac{16}{4}=4$

Thus, $\left(-3,4\right)$ is a solution of equation $\left(i\right)$

Putting $y=\frac{5}{2}$ in equation $\left(i\right)$

$\Rightarrow 3x+4\left(\frac{5}{2}\right)-7=0$

$\Rightarrow 3x=7-10$

$\Rightarrow x=-1$

Thus, $\left(-1,\frac{5}{2}\right)$ is a solution of equation $\left(i\right)$.

Therefore, $\left(1,1\right),\left(2,\frac{1}{4}\right),\left(-3,4\right),\left(-1,\frac{5}{2}\right)$ are four solution of equation $3x+4y=7$.