Question

. Plot a graph for each of the following pairs of equations and shade the region bounded by the 2 lines and the x-axis.
i) x – y + 1 = 0 (ii) 4x – 3y + 4 = 0 (iii) 2x + y = 6
(iv) x + y = 5
2x + y – 10 = 0 4x + 3y – 20 = 0 2x – y + 2 = 0
2x – y +2 =0

Answer 1

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Answer 2

Answer:

The solution for coordinated of shaded area is as below.

Step-by-step explanation:

1.  x – y + 1 = 0 and 2x + y – 10 = 0

By simplifying above equations,

We get equations as :

x = -1 + y and y = 2x - 10

• For x = -1 + y

let x = -1,

then y = 0

let x = 0,

then y = 1

let x = -2,

then y = -1

• For y = 2x - 10

let x = 0,

then y = -10

let x = 1,

then y = -8

let x = 2,

then y = -6

Above are the three points for lines x = -1 + y and y = 2x - 10. By joining these points on graph, we will get the area for shaded region.

2. 4x – 3y + 4 = 0 and 4x + 3y – 20 = 0

By simplifying above equations,

We get equations as :

$\frac{4(x + 4)}{3} = y$  and  $\frac{4(x - 5)}{3} = y$

• For $\frac{4(x + 4)}{3} = y$

let x = 2,

then y = 4

let x = 5,

then y = 8

let x = 8,

then y = 12

• For $\frac{4(x - 5)}{3} = y$

let x = 2,

then y = -4

let x = 8,

then y = 4

let x = -1,

then y = -8

Above are the three points for lines 4x – 3y + 4 = 0 and 4x + 3y – 20 = 0. By joining these points on graph, we will get the area for shaded region.

3. 2x + y = 6 and 2x – y + 2 = 0

By simplifying above equations,

We get equations as :

2x - 6 = -y

2x + 2 = y

• For 2x - 6 = -y

let x = 0,

then y = 6

let x = -1,

then y = 8

let x = 1,

then y = 4

• For 2x + 2 = y

let x = 0,

then y = 2

let x = 1,

then y = 4

let x = -1,

then y = 0

Above are the three points for lines 2x + y = 6 and 2x – y + 2 = 0. By joining these points on graph, we will get the area for shaded region.

4. x + y = 5 and 2x – y +2 =0

By simplifying above equations,

We get equations as :

x = - 5 - y

y = 2x + 2

• For x = - 5 - y

let x = 0,

then y = -5

let x = 5,

then y = -10

let x = -5,

then y = 0

• For y = 2x + 2

let x = 0,

then y = 2

let x = 1,

then y = 4

let x = -1,

then y = 0

Above are the three points for lines x + y = 5 and 2x – y +2 =0. By joining these points on graph, we will get the area for shaded region.

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