Question

Write two solutions for each of the following equations:

(i) $3x+4y=7$ (ii) $x=6y$ (iii) $x+\pi y=4$ (iv) $\frac{2}{3}x-y=4$

Answer 1

(i) $Letx=0,then3\times 0+4y=7\Rightarrow 0+4y=7\Rightarrow 4y=7\Rightarrow y=\frac{7}{4}\therefore x=0,y=\frac{7}{4}\text{are the solutions of the equation.}Lety=0,then3x+4\times 0=7\Rightarrow 3x+0=7\Rightarrow 3x=7\Rightarrow x=\frac{7}{3}\therefore x=\frac{7}{3},y=0\text{are the solutions of the equation.}$

(ii) $Lety=0,thenx=6\times 0=0\therefore x=0,y=0x=0,y=0\text{are the solutions of the equation.}Lety=1,thenx=6\times 1\Rightarrow x=6\therefore x=6,y=1\text{are the solutions of the equation.}$

(iii) $Letx=4,then4+\pi y=4\Rightarrow \pi y=4-4=0\therefore y=0\therefore x=4,y=0\text{are the solutions of the equation.}Letx=0,then0+\pi y=4\Rightarrow \pi y=4\Rightarrow y=\frac{4}{\pi }\therefore x=0,y=\frac{4}{\pi }\text{are the solutions of the equation.}$

(iv) $Letx=0,then\frac{2}{3}\times 0-y=4\Rightarrow 0-y=4\Rightarrow -y=4\Rightarrow y=-4\therefore x=0,y=-4\text{are the solutions of the equation.}Lety=0,then\frac{2}{3}x-0=4\Rightarrow \frac{2}{3}x=4\Rightarrow x=\frac{4\times 3}{2}=6\therefore x=6,y=0\text{are the solutions of the equation.}$