Question

The lines y = 2x, 2x + y - 12 = 0 and y = 2 enclose a triangular region of the xy-plane.

Find
a) the coordinates of the vertices of this region​

Answer 1

the coordinates of the vertices of this region​ are : A(3;6) B(1;2) C(5;2)

Explanation:

look this solution and graph

Answer 2

see explanation

Explanation:

Equate pairs of the equations and solve, that is

y = 2x and y = 2 , hence

2 = 2x ( divide both sides by 2 )

1 = x ⇒ (1, 2)

2x + y - 12 = 0 and y = 2, hence

2x + 2 - 12 = 0

2x - 10 = 0 ( add 10 to both sides )

2x = 10 ( divide both sides by 2 )

x = 5 ⇒ (5, 2)

y = 2x and 2x + y - 12 = 0 ( substitute y = 2x into the second equation )

2x + 2x - 12 = 0

4x - 12 = 0 ( add 12 to both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Substitute x = 3 into y = 2x = (2 × 3 ) = 6 ⇒ (3, 6)

The coordinates of the 3 vertices are

(1, 2 ), (5, 2 ) and (3, 6 )