Iwill give ! the graph shows two lines, a and b:
a graph is shown with x and y axes labelled from 0 to 6 at increments of 1. a straight line labelled a joins the ordered pair 2, 6 with the ordered pair 5, 0. another straight line labelled b joins the ordered pair 0, 2 with the ordered pair 6, 6.
based on the graph, which statement is correct about the solution to the system of equations for lines a and b?
(3, 4) is the solution to both lines a and b.
(3, 4) is the solution to line a but not to line b.
(0, 2) is the solution to both lines a and b.
(0, 2) is the solution to line a but not to line b.

(3, 4) is the solution to both lines A and B.

Step-by-step explanation:

First find the slope of each line by using the slope formula

Slope of A: -2 (passes through (2,6) and (5,0))

Slope of B: 2/3 (passes through (0,2) and (6,6))

Next, find the value of b by plugging each slope value and each corresponding x and y into the point slope equation y=mx+b

Slope A:

(6)=-2(2)+b  I plugged in the point (2,6) but you can also use (5,0).  

6 = -4+b  Next solve for b

10=b, The equation of the line that passes through (2,6) and (5,0) is y=-2x+10

Slope B:

(2)=2/3(0)+b I plugged in the point (0,2) but you can also use (6,6).

2=b, The equation of the line that passes through (0,2) and (6,6) is

y=2/3x+2

Now you can solve for the system of equations using either substitution or elimination.  I will use substitution to first find the value of x.

y=-2x+10

y=2/3x+2

-2x+10=2/3x+2 Solve for x.

8=2 2/3x

x=3

Next plug in x to either of the equations to solve for y.

y=-2(3)+10

y=4, The solution to the system of equations is (3,4)  

To check, plug (3,4) into the equation y=2/3x+2

(4)=2/3(3)+2

4=2+2

4=4  This works therefore, (3, 4) is the solution to both lines A and B.