Final answer:
The y-coordinate of the solution depends on the value of x in the given system of equations. If x = (6 - √84) / 2, the y-coordinate is 11 * ((6 - √84) / 2)
Step-by-step explanation:
The given system of equations is y = 11x and 3y = x^2 + 5x + 12. Since the system has one solution, we can set the two equations equal to each other:
11x = x^2 + 5x + 12
Rearranging the equation, we get:
x^2 - 6x - 12 = 0
To find the x-coordinate of the solution, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from the equation, we get:
x = (-(-6) ± √((-6)^2 - 4(1)(-12))) / (2(1))
Simplifying, we have:
x = (6 ± √(36 + 48)) / 2
x = (6 ± √84) / 2
Now, we can calculate the two possible y-coordinates by substituting the x-values into one of the original equations:
For x = (6 + √84) / 2: y = 11 * ((6 + √84) / 2)
For x = (6 - √84) / 2: y = 11 * ((6 - √84) / 2)
Therefore, the y-coordinate of the solution depends on the value of x:
If x = (6 + √84) / 2, the y-coordinate is 11 * ((6 + √84) / 2)
If x = (6 - √84) / 2, the y-coordinate is 11 * ((6 - √84) / 2)