Question

Write two solutions of the form $x=0,y=1andx=b,y=0$ for each of the following equations:

(i) 5x - 2y = 10 (ii) - 4x + 3y = 12 (iii) 2x + 3y = 24

Answer 1

(i) 5x - 2y = 10

Let x = 0, then

$5\times 0-2y=10\Rightarrow -2y=10\Rightarrow y=\frac{10}{-2}=-5\therefore x=0,y=-5\text{are the solutions of the equation}Lety=0,then5x-2\times 0=10\Rightarrow 5x=10\Rightarrow x=\frac{10}{5}=2\therefore x=2,y=0\text{are the solutions of the equation.}$

$\left(ii\right)-4x+3y=12Letx=0,then-4\times 0+3y=12\Rightarrow 3y=12\Rightarrow y=\frac{12}{3}=4\therefore x=0,y=4\text{are the solutions of the equation}Lety=0,then-4x+3\times 0=12\Rightarrow -4x=12\Rightarrow x=\frac{12}{-4}=-3\therefore x=-3,y=0\text{are the solutions of the equation.}$

$\left(iii\right)2x+3y=24Letx=0,then2\times 0+3y=24\Rightarrow 3y=24\Rightarrow y=\frac{24}{3}=8\therefore x=0,y=8\text{are the solutions of the equation}Lety=0,then2x+3\times 0=24\Rightarrow 2x=24\Rightarrow x=\frac{24}{2}=12\therefore x=12,y=0\text{are the solutions of the equation}$