PLZ ANSWER QUICK: The graph shows two lines, A and B:

A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 3, 0, and the ordered pair 0, 6. Another straight line labeled B joins the ordered pair 0, 0, and the ordered pair 5, 5.

Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
0, 6) is the solution to both lines A and B.
(0, 6) is the solution to line B but not to line A.
(2, 2) is the solution to both lines A and B.
(2, 2) is the solution to line A but not to line B.

Choice D

(2,2) is the solution to line A, but not to line B

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Explanation:

Let's find the equation of line A

First we need the slope

m = (y2-y1)/(x2-x1)

m = (6-0)/(0-3)

m = 6/(-3)

m = -2

Since the point (0,6) is on line A, we know b = 6 is the y intercept.

The equation of line A is y = -2x+6.

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Let's find the equation for line B

So we need the slope

m = (y2-y1)/(x2-x1)

m = (5-0)/(5-0)

m = 5/5

m = 1

The y intercept is b = 0 since the line goes through (0,0)

The equation of line B is y = 5x+0 which is the same as y = 5x.

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Our system of equations is

We can see that plugging x = 0 into line A's equation leads to y = 6. So (0,6) is on line A. However, the point (0,6) is not on line B because plugging x = 0 leads to y = 0.

This allows us to rule out choices A and B.

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Let's see what happens when we plug in x = 2 to line A

y = -2x+6

y = -2*2+6

y = -4+6

y = 2

The point (2,2) is on line A

Now let's do the same for line B

y = 5x

y = 5*2

y = 10

The point (2,10) is on line B meaning that (2,2) is not on line B.

We can rule out choice C and conclude that choice D is the final answer.

Side note: Choice D should read "(2,2) is a solution" instead of "(2,2) is the solution" since there are infinitely many solutions on any given line. So another solution for example would be (0,6).

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4