Question

Solve the following system of linear equations graphically: 2x-8-y;x-y-1=0. Shade the region bounded by these two lines and y-axis. Also, find the area of shaded part.​

Answer 1

Answer :-

2x - 8 - y;

x - y - 1 = 0

Heyo! We can find the values on the graph as follows;

#ReferTheAttachement

★ More Information :-

$\mapsto$ Graph informations are mainly dependent on the values given. The value may be negative or positive integers. They can also be 0.

Answer 2

Given

• 2x+y=8
• x-y-1=0 or x-y=1

To Find

• Shade the region bounded by these two lines and y-axis. Also, find the area of shaded part.

Solution

____________________

• 2x+y = 8 ___(1)

put x = 0

$\\ ~~~\sf~~\implies ~~ 2×0+y=8$

$~~~\sf~~\implies y=8$

Put x = 1

$\\ ~~~\sf~~\implies ~~ 2×1+y=8$

$~~~\sf~~\implies ~~ 2+y=8$

$~~~\sf~~\implies ~~ y=8 - 2$

$~~~\sf~~\implies ~~ y=6$

Put x = 2

$\\ ~~~\sf~~\implies ~~ 2×2+y=8$

$~~~\sf~~\implies ~~ 4+y=8$

$~~~\sf~~\implies ~~ y=8 - 4$

$~~~\sf~~\implies ~~ y=4$

$~~~~~\sf{\begin{array}{ | c | c | c | c | }\hline \sf x & 0 & 1 &2\\\hline \sf y & 8 &6&4 \\ \hline \end{array}}$

____________________

• x - y = 1

Put x = 0

$\\ ~~~\sf~~\implies ~~ 0 - y = 1$

$~~~\sf~~\implies ~~ y = - 1$

Put x = 1

$\\ ~~~\sf~~\implies ~~ 1 - y = 1$

$~~~\sf~~\implies ~~ - y = 1 - 1$

$~~~\sf~~\implies ~~ y = 0$

Put x = 2

$\\ ~~~\sf~~\implies ~~ 2 - y = 1$

$~~~\sf~~\implies ~~ - y = 1 - 2$

$~~~\sf~~\implies ~~ - y = - 1$

$~~~\sf~~\implies ~~ y = 1$

$~~\sf~~~~\begin{array}{ | c | c | c | c | }\hline \sf x & 0 & 1 &2\\\hline \sf y & - 1 & 0&1 \\ \hline\end{array}$

___________________

Solution, x= 3 and y = 2

Area of x= 3 and y = 2

Area of ABCD = 1/2 Base × Height

Area of ABCD = 1/2 × 9 × 3

Area of ABCD = 4.5 × 3

Area of ABCD = 13.5 sq.units