Question

#13. What is the solution to this system of equations? y= 1 3​x+4 y= 1 6​x+3

Answer 1

is it (6,0) or (2,2) or (0,2)

Answer 2

To find the solution to this system of equations, we need to set the two equations equal to each other since they both equal y.

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

Multiplying the entire equation by 6 to get rid of the fractions gives us:

2x + 24 = x + 18

Now, subtract x from both sides:

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

Then, subtract 24 from both sides to solve for x:

x = 18 - 24
x = -6

Now, substitute x = -6 back into one of the original equations (e.g., y = 1/3x + 4) to solve for y:

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

Therefore, the solution to this system of equations is x = -6 and y = 2.

Answer 3

Let's double check the solution. We found that x = -6 and y = 2. Let's substitute these values back into the second equation y = 1/6x+3 to verify the solution.

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

So, the second equation also satisfies the solution.

Therefore, the solution to the system of equations y = 1/3x + 4 and y = 1/6x + 3 is x = -6 and y = 2, written as the ordered pair (-6, 2).