Question

What are the solutions of the system? Solve by graphing.

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

Answer 1

Solutions are (0,2) and (-1,4).

Explanation:

There are two equations given for which graphing is to be done.

Equations are y = -2x+2------(1)

and y = -x²-3x+2---------(2)

Now we will solve the equations to get the values of x and y or the coordinates of intersection of these two graphs.

By substituting y from equation 2 into equation 1.

- x²-3x+2 = -2x+2

-x²-3x+2x = 0

-x²-x = 0

x²+x = 0

x(x+1)=0 ⇒ x = 0 and x = -1

Now we put these values of x in equation 2.

For x = 0 y = -2×0+2 = 2

For x = -1 y = 2+2 = 4

So they intersect each other at (0,2) and (-1,4).