SOLUTION: How do I solve the follwoing system of equations? y = {{{ sqrt (x) }}}+ 4 y = 2x + 1 Can you provide a detailed answer showing all of the steps?

Question 188800: How do I solve the follwoing system of equations?
y = + 4
y = 2x + 1

Can you provide a detailed answer showing all of the steps?
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the first equation.

Plug in

Subtract 4 from both sides.

Combine like terms.

Square both sides

FOIL

Subtract x from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers for "x" are or

However, if you plug in into the equation , you'll find a contradiction. So this is an extraneous solution (ie we must ignore this value).

So the only solution for "x" is

Now plug in into to find "y"

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How do I solve the follwoing system of equations?
y = + 4
y = 2x + 1
------------
There's more than one way, but since both right sides = y, I'd set them equal to each other.
2x+1 = sqrt(x) + 4
sqrt(x) = 2x-3
x = 4x^2 - 12x + 9
4x^2 - 13x - 9 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=313 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.83647575161927, -0.586475751619266. Here's your graph:

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