Question

Draw the graphs the equations x-y = 1 and, 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine this area.

Answer 1

Answer:

Write the equation x-y=1 as

y = x - 1

and the equation 2x+y=8 as

y = -2x + 8

Choose any two value of x and use them to calculate the values of x.

Plot these points for both lines and join them using a straight line.

See the attached image

The two lines and the y-axis for a triangle with base = 9 units and height = 3 units

Area of triangle = 1/2 base x eight

= 1/2 x 9 x 3

= 13.5 sq. units

Step-by-step explanation:

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Answer 2

Answer:

AREA = 13.5 sq. units

Step-by-step explanation:

equation 1 : x - y = 1

let x = 0,

x - y = 1

0 - y = 1

y = -1

let y  = 0,

x - y = 1

x - 0 = 1

x = 1

∴ coordinates for x - y = 1 are  A (0, -1) and

B (1,0)

equation 2 : 2x + y = 8

let x = 0

2x + y = 8

2(0) + y = 8

y = 8

let y = 0

2x + y = 8

2x + 0 = 8

x = 4

∴ coordinates for 2x + y = 8 are C (0,8) and

D (4,0)

SHADED REGION IS A TRIANGLE.

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

=> $\frac{1}{2}$ × 9 × 3 = 13.5 sq unit