Question

Help me please I need answers

Answer 1

The solution of the system of equations are;

(-2, -6) and (4, 6)

Explanation:

-2·x + y = -2...............(1)

`y = -(1)/(2) \cdot x^2 + 3 \cdot x + 2`........(2)

Equation (1) gives;

y = 2·x - 2

From which we have;

`2 \cdot x - 2 = -(1)/(2) \cdot x^2 + 3 \cdot x + 2`

`0= -(1)/(2) \cdot x^2 + x + 4`

x² -2·x -8 = 0

(x - 4)·(x + 2) = 0

x = 4 or x = -2

The y-coordinate values are;

y = 2×(-2) - 2 = -6 and y = 2×(4) - 2 = 6

The solution points are;

(-2, -6) and (4, 6).

The points where the equation, -2·x + y = -2 and the equation
`y = -(1)/(2) \cdot x^2 + 3 \cdot x + 2` intersect are (-2, -6) and (4, 6).