Question

Find the vertice of the triangle x+y=10 , 2x+3y=5, 6x-y=11

Answer 1

Answer:

(1.9, 0.4), (3, 7), (25, -15)

Step-by-step explanation:

Coordinates of the vertices of the triangle are solutions of systems of pairs of linear equations:

1). x + y = 10 and 2x + 3y = 5

2). x + y = 10 and 6x - y = 11

3). 2x + 3y = 5 and 6x - y = 11

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1). x + y = 10 ..... (1)

2x + 3y = 5 ..... (2)

(1)×2 - (2)

- y = 15 ⇒ y = - 15

x - 15 = 10 ⇒ x = 25

Coordinates of first vertex are (25, - 15)

2). x + y = 10 .... (1)

6x - y = 11 ..... (2)

(1) + (2)

7x = 21 ⇒ x = 3

3 + y = 10 ⇒ y = 7

Coordinates of second vertex are (3, 7)

3). 2x + 3y = 5 ..... (1)

6x - y = 11 ..... (2)

(2)×3 + (1)

20x = 38 ⇒ x = 1.9

11.4 - y = 11 ⇒ y = 0.4

Coordinates of third vertex are (1.9, 0.4)