Question

Solve the following system of linear equations graphically and shade the region between two lines and $x$-axis:

(i) $3x+2y-4=0$

$2x-3y-7=0$

(ii) $3x+2y-11=0$
$2x-3y+10=0$

Answer 1

The given equations are:

(i)

$3x+2y-4=0$...(1)

$2x-3y-7=0$...(2)

put $x=0$ in (1),

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

$y=2$

put $y=0$ in (2),

$2x-3\left(0\right)-7=0$

$x=\frac{7}{2}$

put $x=0$ in (2),

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

$y=-\frac{7}{3}$

put $y=0$ in (1),

$3x+2\left(0\right)-4=0$

$x=\frac{4}{3}$

$(x=0,y=-\frac{7}{3})$

$(x=\frac{4}{3},y=0)$

$(x=0,y=2)$

$(x=\frac{7}{2},y=0)$

(ii)

$3x+2y-11=0$...(1)

$2x-3y+10=0$...(2)

put $x=0$ in (1),

$3\left(0\right)+2y-11=0$

$y=\frac{11}{2}$

put $y=0$ in (2),

$2x-3\left(0\right)+10=0$

$x=-5$

put $x=0$ in (2),

$2\left(0\right)-3y+10=0$

$y=\frac{10}{3}$

put $y=0$ in (1),

$3x+2\left(0\right)-11=0$

$x=\frac{11}{3}$

$(x=\frac{11}{3},y=0)$

$(x=0,y=\frac{10}{3})$

$(x=0,y=\frac{11}{2})$

$(x=-5,y=0)$