The three straight lines y = x, 7y = 2x, and 4x + y = 60 form a triangle. Find t

ringearV

ringearV

Answered question

2021-08-17

The three straight lines y = x, 7y = 2x, and 4x + y = 60 form a triangle. Find the coordinates of its vertices.

Answer & Explanation

SchulzD

SchulzD

Skilled2021-08-18Added 83 answers

The coordinates of the vertices are the points of intersection of the lines taken two at a time.
Using(1)y=x and (2) 7y=2x, we substitute (1) to (2) and solve for x:
7x=2x
5x=0
x=0
Using(1), we solve for y:
y=0
So, one vertex of the triangle is at (0,0).
Using(1)y=x and (3)4x+y=60, we substitute(1) to (3) and solve for x:
4x+x=60
5x=60
x=12
Using (1), we solve for y:
y=12
So, another vertex of the triangle is at (12,12)
Using (2)7y=2x and (3) 4x+y=60, we first solve for y using (2) to obtain (4):
y=27x
Substitute (1) and (3) and solve for x:
4x+27x=60
307x=60
x=60730
x=14
Using(4), we solve for y:
y=27(14)
y=4
So, another vertex of the triangle is at (14,4).
Result: (0,0), (12,12),(14,4)

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