Find the solutions of the system:

y = x^2 - 3x + 2

Y=2x + 2

(1 point)
Responses

(0,1) and (6,4)
(0,1) and (6,4)

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

(1,0) and (4,6)
(1,0) and (4,6)

No Solution
No Solution

1 answer

To find the solutions of the system, we can set y = y and solve for x:

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

Rearranging the equation, we get:

x^2 - 5x + 0 = 0

Factoring the quadratic equation:

x(x - 5) = 0

Setting each factor to 0:

x = 0 or x = 5

Now substituting each value of x back into the second equation y = 2x + 2, we get:

If x = 0,
y = 2(0) + 2
y = 2
So, one solution is (0, 2).

If x = 5,
y = 2(5) + 2
y = 10 + 2
y = 12
So, the other solution is (5, 12).

Therefore, the solutions of the system are (0, 2) and (5, 12).