What are the solutions of the system? solve by graphing. y = x^2 + 3x + 2 y = 2x + 2

y=x2−2x−1y=x2-2x-1y=−2

When graphing a system by graphing, you will get two lines, and the point where these lines intersect is considered the solution. Solving by substitution gives you the coordinates of this point, without having to graph these lines. Regardless of the method, substituting the solution into the system for x and y will yield two equations that can be verified as true.

Vertex of x^2-2x-1 is (1,-2) so B is true

To solve this problem you must:

 1. Rewrite the equations:

 y=x²-2x-1  (i)
 
 y=-2  (ii)

 2. Then: 

 (i)=(ii)

 -2=x²-2x-1

 3. Now, you must order the terms and and factorize, as below:

 (x-1)(x-1)=0
 (x-1)²=0

 4. The solution is:

 x=1

 You can see that the graphs attached touch each other in x=1. Therefore, the solution is x=1
 
 

It's easy to see from the graph that they intersect at (1,-2).

I used desmos online.

(1,-2)

Solutions of the given equations is (-3,2).

Step-by-step explanation:

Here the equations given are y = -x²-6x-7------(1)

and y = 2---------(2)

Now we substitute the value of y from equation (2) into (1)

2 = -x²-6x-7

x²+6x+7 = -2

x²+6x+7+2 = 2-2

x²+6x+9 = 0

x²+3x+3x+9 = 0

x(x+3)+3(x+3) = 0

(x+3)(x+3) = 0

therefore value of x is x = -3

Therefore the solution is (-3,2).

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

Step-by-step 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).

(-3, 2)

Step-by-step explanation:

1. When you grapth the parabola given by the first equation and the line given by the second equation, you obtain the graph shown in the figure attached.

2. To know the solution of the system of equations, you must see the point where the parabola and the line intersect. As you can see the point is at (-3,2), so that is the solution.

hello : two solutions (0;2) , (-1;0)

Step-by-step explanation:

two solutions (0;2) , (-1;0)

points intersection the curve (y = x²+3x+2) and the line ( y =2x+2)