Question

Find the solutions to the system: {y=x²-9x+12, y=3x+4}

a) (-3, -3)
b) (-2, 2)
c) (4, 16)
d) (5, 19)

Answer 1

To find the solutions to the system of equations {y=x²-9x+12, y=3x+4}, we can set the two equations equal to each other and solve for x. Using the quadratic formula, we find that x=4 and x=2 are the solutions. Substituting these values back into either equation, we find the corresponding y-values.

Step-by-step explanation:

To find the solutions to the system of equations {y=x²-9x+12, y=3x+4}, we can set the two equations equal to each other and solve for x.

x²-9x+12 = 3x+4

Combining like terms and rearranging the equation, we get:

x²-12x+8 = 0

We can then use the quadratic formula to solve this equation:

x = (-b ± √(b²-4ac))/(2a)

where a = 1, b = -12, and c = 8. Plugging in the values, we get two solutions: x = 4 and x = 2. Substituting these values back into either of the original equations, we can find the corresponding y-values:

When x = 4, y = 3(4) + 4 = 16+4 = 20. So, one solution is (4, 20).

When x = 2, y = 3(2) + 4 = 6+4 = 10. So, another solution is (2, 10).