What is the solution to this system of equations?

Question

Y=1/3x +4
y=1/6x+3
A. (0,2)
B. (2,2)
C. (-6,2)
D. (6,0)

Answer 1

To find the solution to this system of equations, we can set the two equations equal to each other and solve for x:

1/3x + 4 = 1/6x + 3

To get rid of the fractions, we can multiply both sides of the equation by 6:

6(1/3x + 4) = 6(1/6x + 3)
2x + 24 = x + 18

Now, we can subtract x from both sides of the equation:

2x - x + 24 = x - x + 18
x + 24 = 18

Next, we can subtract 24 from both sides of the equation:

x + 24 - 24 = 18 - 24
x = -6

Now that we know x = -6, we can substitute this value back into one of the original equations to solve for y. Let's use the first equation:

y = 1/3(-6) + 4
y = -2 + 4
y = 2

So the solution to this system of equations is (-6, 2), which corresponds to option C.