Question

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?

A (0, 6) is the solution to both lines A and B.
B(0, 6) is the solution to line B but not to line
C(2, 2) is the solution to both lines A and B.
D (2, 2) is the solution to line A but not to line

Answer 1

C(2, 2) is the solution to both lines A and B.

Explanation:

Line A is given as:

A straight line labeled A joins the ordered pair 3, 0 and the ordered pair 0, 6.

We know that the equation of a line passing through (a,b) and (c,d) is calculated as:

`y-b=(d-b)/(c-a)* (x-a)`

Hence, the equation of line is:

`y-0=(6-0)/(0-3)* (x-3)\\\\y=(6)/(-3)* (x-3)\\\\y=-2* (x-3)\\\\y=-2x+6`

Hence, equation of line A is:

`y=-2x+6`

Similarly B is a line passing through (0,0) and (5,5).

Hence, the equation of line B is:

`y=x`

So, from the graph we observe that, the point of intersection of the two lines is (2,2).

Thus, option C is correct.

Answer 2

The correct answer for the question that is being presented above is this one: "A (0, 6) is the solution to both lines A and B." The statement that is correct about the solution to the system of equations for lines A and B is that (0, 6) is the solution to both lines A and B.