Three Straight Lines(equations) form a triangle. Find the coordinates of its vertices.?

Question

Please show me how to work this maths problem out. Thanks.

The three straight lines

1. y=x
2. 7y=2x
3. 4x+y=60

Answers
(0,0) (12,12) (14,4)

Answer 1

Systems of equations between each two of the lines shown.

Let's take y=x and 7y=2x
It has to be (0,0) because it's the only solution that satisfies it.

Then y=x and 4x+y=60
4x+x=60
x=12
4(12)+y=60
48+y=60
y=12
So it's (12,12).

7y=2x and 4x+y=60
2(7y)+y=60
15y=60
y=4
7(4)=2x
28=2x
x=14
So it's (14,4)

Answer 2

The best thing to do with a problem like this is to do some sketching to see what it looks like. The triangle you get is not the friendly one you see with the base resting on a horizontal line. First, x=y and y= (2/7) x intersect at the origion, since neither has an x-intercept. x=y has a slope of 1, and y= (2/7) x has a flatter slope of +2/7. The third line, in slope-intercept form, is y = 60-4x. So this line will cross the x-axis at y=60 with a -4 slope. It will first intersect with the x=y line. At this intersection, since x=y, y=60-4y, and y=12. Also, x=12. Then y=60-4x will intersect with y= 2/7 x.
At this point, (2/7) x = 60-4x, or 30x/7 = 60. Then, x=14, and y= 4.

Answer 3

the place does y=x meet 7y=2x? for sure (0,0). the place does y=x meet 4x+y=60 ? 4x+x=60 5x=60 x=12 y=x=12 answer (12, 12). the place does 7y=2x meet 4x+y=60? Multiply the 1st equation by potential of two. 14y = 4x 14y + y = 60 15y = 60 y=4 substitute this into 7y=2x to get 28=2x so x=14. answer (14, 4). The vertices are (0,0) and (12,12) and (14,4). i desire this helps.

Answer 4

The three vertices are the intersections of the lines taken two at a time.