Question

Draw the graph of the system of equation x+y=5 and 2x -y +2=0 Shade the region bounded these lines and the x axis. Find the area the shaded ongion of​

Answer 1

Answer:

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Answer 2

Answer:

Region enclosed between $ABC$ is the required shaded region.

Area of shaded region is 12 sq. units.

Step-by-step explanation:

Consider the system of equations as follows:

$x+y=5$ . . . . . (1)

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

(i) Two solutions of equation (1) are:

If $x=0$, then $y=5$.

If $y=0$, then $x=5$.

So, $(0,5)$ and $(5,0)$ are the solution of the equation $x+y=5$.

(ii) Two solutions of equation (2) are:

If $x=0$, then $y=2$.

If $y=0$, then $x=-1$.

So, $(0,2)$ and $(-1,0)$ are the solution of the equation $2x-y+2=0$.

Thus, the graph is sketched using the solution of equations.

Region enclosed between $ABC$ is the required shaded region.

From the graph,

In Δ$ABC$,

Base, $BC=6$ units

Height, $AD=4$ units

Area of shaded region = $\frac{1}{2}$ × base × height

                                      = $\frac{1}{2}$ × 6 × 4

                                      = 12 sq. units.

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