Question

Consider the system of equations.

Answer 1

The solution of the system of equations are the points (-2,-6) and (4,6)

Explanation:

we have

`-2x+y=-2` ----> equation A

`y=-(1)/(2)x^(2)+3x+2` ----> inequality B

we know that

The solution of the system of equations is the intersection point both graphs

To graph the linear equation, find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

`-2(0)+y=-2`

`y=-2`

The y-intercept is the point (0,-2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

`-2x+0=-2`

`x=1`

The x-intercept is the point (1,0)

Plot the intercepts to graph the linear equation and find the intersection points with the quadratic equation

The intersection points are (-2,-6) and (4,6)

see the attached figure

therefore

The solution of the system of equations are the points (-2,-6) and (4,6)