Solve the system of equations algebraically. Show all of your steps.
Y=x^2+2x
Y=3x+20
To solve the system of equations, we need to find the values of x and y that satisfy both equations. Since both equations are equal to y, we can set them equal to each other:
x^2 + 2x = 3x + 20
Now we can solve for x by getting all the terms on one side of the equation:
x^2 + 2x - 3x - 20 = 0
x^2 - x - 20 = 0
Now let's factor the quadratic equation:
(x - 5)(x + 4) = 0
This gives us two possible solutions for x:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Now we need to find the corresponding y values for each x value. We can use either equation, but let's use the first one since it's simpler:
If x = 5:
Y = (5)^2 + 2(5)
Y = 25 + 10
Y = 35
If x = -4:
Y = (-4)^2 + 2(-4)
Y = 16 - 8
Y = 8
So we have two solutions for the system of equations: (5, 35) and (-4, 8).