Solve the system of equations algebraically. Show all of your steps.

Question

y=x^2+2x
y=3x+20
Can I get a good explanation? Like I know how the steps look after the first breakdown but by the second Nobody exactly explains what was added or subtracted to get to it.
like what did you do to remove the 2x and the 3x?

Answer 1

To solve the system of equations algebraically, we can set the two equations equal to each other and solve for x:

x^2 + 2x = 3x + 20

Next, we can move all terms to one side of the equation to set it equal to zero:

x^2 + 2x - 3x - 20 = 0
x^2 - x - 20 = 0

Now, we can factor the quadratic equation:

(x + 4)(x - 5) = 0

Setting each factor equal to zero, we find:

x = -4, x = 5

Now, to find the corresponding values of y, we substitute the x-values back into one of the original equations. Let's use y = x^2 + 2x:

For x = -4:
y = (-4)^2 + 2(-4)
y = 16 - 8
y = 8

So, the solution for x = -4 is y = 8.

For x = 5:
y = 5^2 + 2(5)
y = 25 + 10
y = 35

So, the solution for x = 5 is y = 35.

Therefore, the solutions to the system of equations are x = -4, y = 8 and x = 5, y = 35.