Create a system of equations that includes one linear equation and one quadratic equation.

Part 1. Show all work to solving your system of equations algebraically.
Part 2. Graph your system of equations, and show the solution graphically to verify your solution.

is that the answer?

y = x^2 + 3x + 5

y = x + 13

solution:
x^2 + 3x + 5 = x + 13
x^2 + 2x -8 = 0
(x+4)(x-2) = 0
x = -4 or x = 2

if x = -4, y = 9
if x = 2 , y = 15

http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+%2B+3x+%2B+5,+y+%3D+x+%2B+13

ummmhhh, yes

is it right ?

ok ty

WHats part 2?

Part 1: Solving the System of Equations Algebraically

Step 1: Create the linear equation.
Let's say the linear equation is:
y = 2x + 3

Step 2: Create the quadratic equation.
Let's say the quadratic equation is:
y = x^2 - 4

Step 3: Solve the system of equations algebraically by substituting one equation into the other.

Substitute equation (1) into equation (2):
2x + 3 = x^2 - 4

Rearrange the equation:
x^2 - 2x - 7 = 0

Step 4: Solve the quadratic equation using factoring, completing the square, or the quadratic formula.

In this case, let's solve the equation by factoring.
(x - 3)(x + 1) = 0

Setting each factor equal to zero:
x - 3 = 0 or x + 1 = 0

Solving for x:
x = 3 or x = -1

Step 5: Substitute the values of x back into one of the original equations to solve for y.

For x = 3:
y = 2(3) + 3
y = 6 + 3
y = 9

For x = -1:
y = 2(-1) + 3
y = -2 + 3
y = 1

So, the solutions for the system of equations are:
(x, y) = (3, 9) and (-1, 1)

Part 2: Graphing the System of Equations

To graph the system of equations, plot the points (3, 9) and (-1, 1) on a coordinate plane. Then, graph the linear equation y = 2x + 3 and the quadratic equation y = x^2 - 4. The solution to the system of equations is the point(s) where the graphs intersect.

Here is a graph showing the linear equation y = 2x + 3 (in blue) and the quadratic equation y = x^2 - 4 (in red):
[Graph]

As we can see, the blue line intersects the red curve at the points (3, 9) and (-1, 1), which confirms the solution to the system of equations obtained algebraically.