What is area x+2y=2,y-x=1,2x+y=7 ?

The answer to area x+2y=2,y-x=1,2x+y=7 is 6

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area x+2y=2,y-x=1,2x+y=7

area

x + 2 y = 2, y - x = 1, 2 x + y = 7

6

Solution steps

Isolate

y

for

x + 2 y = 2 : y = \frac{2 - x}{2}

Isolate

y

for

y - x = 1 : y = 1 + x

Isolate

y

for

2 x + y = 7 : y = 7 - 2 x

f_{1} (x) = \frac{2 - x}{2}

f_{2} (x) = 1 + x

To find the intersection points solve

f_{i} (x) = f_{j} (x)

\frac{2 - x}{2} = 1 + x : x = 0

\frac{2 - x}{2} = 7 - 2 x : x = 4

1 + x = 7 - 2 x : x = 2

= \int_{0}^{2} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{2}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{2} \frac{2 - x}{2} - (1 + x) d x + \int_{2}^{4} \frac{2 - x}{2} - (7 - 2 x) d x

\int_{0}^{2} \frac{2 - x}{2} - (1 + x) d x = 3

\int_{2}^{4} \frac{2 - x}{2} - (7 - 2 x) d x = 3

= 3 + 3

Simplify

= 6