Explain how to solve the system of equations algebraically.

Solve the system of equations.

Question

Explain how to solve the system of equations algebraically.

Solve the system of equations.

oraclethinktank · Answer

Based on my assignment, I have to solve the quadratic equation by either Factoring, using the Square Root Method, Completing the Square, or by used the Quadratic Formula. The linear equation would be solved as any other one of course. Then I simply explain how to solve the system which would be telling what form I used to solve the Quadratic Equation, and how I solved the Linear Equation.

oraclethinktank · Answer

This is the System.

legomyego180 · Answer

What are you looking for exactly here?

legomyego180 · Answer

The coordinates of the intersection?

oraclethinktank · Answer

I believe. I have to solve the system of equations. The system consists of a Linear Equation and a Quadratic Equation. The linear equation I believe is to be solved like normal, but the Quadratic Equation needs to be solved by either Factoring, using the Quadratic Formula, Completing the Square, or using the Square Root Method.

oraclethinktank · Answer

So it would be solving the system, then explain how I solved it, meaning I solved the Linear equation and how I solved the Quadratic Equation.

legomyego180 · Answer

So you want to set these equations equal to each other, and to do that you need to solve the top equation for y

legomyego180 · Answer

Doing that you'll get y=2-x

legomyego180 · Answer

plug that y value into your second equation so you can get all of the y's out of the second equation.

oraclethinktank · Answer

How would I plug it in? Would it be 2 = -1/4 x^2 + 3?

legomyego180 · Answer

$$2-x=-\frac{ 1 }{ 4 }x^2+3$$

Get all terms on one side so you can set up your quadratic:

$$2=-\frac{ 1 }{ 4 }x^2+3+x$$
$$0=-\frac{ 1 }{ 4 }x^2+3+x-2$$
$$0=-\frac{ 1 }{ 4 }x^2+x+1$$

(Note $x^2+x+1$ will factor)

oraclethinktank · Answer

So the equation is best solved by factoring the Quadratic Equation?

legomyego180 · Answer

$$-\frac{ 1 }{ 4 }(x+2)^2=-\frac{ 1 }{ 4 }x^2+x+1$$
$$-\frac{ 1 }{ 4 }(x+2)=0$$
$$x+2=0$$
x=-2

Factoring.

oraclethinktank · Answer

Wouldn't that mean that y = 4 though?

oraclethinktank · Answer

Since x + y = 2, if x = -2, then y would have to be 4

legomyego180 · Answer

yup

legomyego180 · Answer

(-2,4)

If you plug -2 into either equation you will get four, which means this is where they intersect

legomyego180 · Answer

Hold on, something doesnt seem right.

legomyego180 · Answer

@zepdrix

legomyego180 · Answer

There should be more than one intersection. Sorry, Im not the best at algebra.