Question

Find the solutions of the system:

y = x^2 - 3x + 2

Y=2x + 2

Responses

(0,1) and (6,4)

(0,2) and (0,-2)

(1,0) and (4,6)

No Solution

Answer 1

To find the solutions of the system, we need to set the two equations equal to each other:

x^2 - 3x + 2 = 2x + 2

Rearranging terms:

x^2 - 3x - 2x + 2 - 2 = 0
x^2 - 5x + 0 = 0

Factoring:

x(x - 5) = 0

Setting each factor equal to zero:

x = 0 or x - 5 = 0
x = 0 or x = 5

Now plug these values of x back into one of the original equations (easier to use y=2x+2):

For x = 0:
y = 2(0) + 2
y = 2
So, one of the solutions is (0, 2)

For x = 5:
y = 2(5) + 2
y = 12
So, the other solution is (5, 12)

Therefore, the solutions of the system are (0,2) and (5,12). None of the given responses match these solutions.