Question

Consider the system of equations.

Answer 1

Answer:

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

Step-by-step explanation:

we have

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

$y=-\frac{1}{2}x^{2}+3x+2$ ----> 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)