Question

Solve the system of inequalities graphically:

$5x+4y$$\le$ $20,x$$\ge$$1,y$ $\ge$$2$

Answer 1

First we solve $5x+4y\ge 20$

Let first draw graph of

$x$ $0$ $4$

$y$ $5$ $0$

$5x+4y=20$ ___(1)

Putting $x=0$ in (1)

$5\left(0\right)+4y=20$

$0+4y=20$

$4y=20$

$y=\frac{20}{4}$

$y=5$

Putting $y=0$ in (1)

$5x+4\left(0\right)=20$

$5x+0=20$

$5x=20$

$x=\frac{20}{5}$

$x=4$

Drawing graph

$x$ $0$ $4$

$y$ $5$ $0$

Points to be plotted are $(0,5),(4,0)$

Checking for $(0,0)$

$5x+4y\le 20$

Putting $x=0,y=0$

$5\left(0\right)+4\left(0\right)\le 20$

$0\le 20$

Which is true

Hence origin lies in plane $5x+4y\le 20$

So, we shade left side of line

REF. IMAGE 1

Also, $y\ge 2$

So, for all values of

$x,wherey=2$

$x$ $0$ $-1$ $4$

$y$ $2$ $2$ $2$

Points to be plotted are $(0,2),(-1,2),(4,2)$

Also, $x\ge 1$

So, for all values of $y,wherex=1$

$x$ $1$ $1$ $1$

$y$ $0$ $-1$ $3$

Point to be plotted are $(1,0),(1,-1),(1,3)$

Hence the shaded region represents the given in equality

REF. IMAGE 2

Shaded region shows the intersection of given inequality.