Question

solve the following system of linear equation graphically: 3x+y-11=0 and x-y-1=0
shade the region bounded by these lines and the y-axis. Find the co-ordinates of points where the line cuts the y-axis.

Answer 1

Step-by-step explanation:

Given:

$3x + y - 11 = 0 \\ \\ x - y - 1 = 0$

To find:

1. Solve the following system of linear equation graphically.
2. Shade the region bounded by these lines and the y-axis.
3. Find the co-ordinates of points where the line cuts the y-axis.

Solution:

1) Solve the following system of linear equation graphically.

Find at least two points of each equation

$3x + y = 11$

put x=0;y=11 ; (0,11)

put y=0;x=11/3; (11/3,0)

$x - y = 1$

put x=0;y=-1; (0,-1)

Put y=0,x=1 ;(1,0)

plot these points and common point is the solution of linear equations.

(See attached graph)

2) Region is shaded; see the attatched graph 2

3) Coordinates of the points where lines cuts y-axis

(0,-1)

(0,11)

Final answer:

1)Solution of linear equations is x=3 and y=2.

2)Shaded area is attatched.

3) Points of intersection of y-axis are (0,-1),(0,11)

Hope it helps you.

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Answer 2

Given data:

Linear equations,

• $3x+y-11=0$

• $x-y-1=0$

To find:

Solution by graphical method

Shade the region bounded by the given lines and the $y$-axis

Coordinates of points where the lines cut the $y$-axis

Step-by-step explanation:

The given lines are

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

$\quad x-y-1=0$ . . . (2)

Step 1. Finding points to plot the lines

The first line is $3x+y-11=0$

• Let $x=0$. Then $y=11$
• Let $x=1$. Then $y=7$

So we have a pair of points $(0,11)$ and $(1,7)$.

Plot these points on the graph paper and join them to draw the first line.

The second line is $x-y-1=0$

• Let $x=0$. Then $y=-1$
• Let $x=1$. Then $y=0$

So we have a pair of points $(0,-1)$ and $(1,0)$.

Plot these points on the graph paper and join them to draw the second line.

Step 2. Finding the intersection of the two lines

We see that the two line intersect each other at the point $(3,2)$

Thus the required solution obtained graphically is

$\quad x=3,y=2$

Step 3. Shading the bounded region

We see that each of the given lines intersect the $y$-axis at a point and they make a bounded region. We shade them.

Step 4. Points where the lines intersect

We see that the line $3x+y-11=0$ intersect the $y$-axis at $(0,11)$ and the line $x-y-1=0$ intersect the $y$-axis at $(0,-1)$.

Answers: Refer to the given picture.

• Solution, $x=3,y=2$
• Bounded region shaded
• Points, $(0,11),(0,-1)$

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