Answer:
(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.
