OpenStudy (anonymous):

Will someone please help me? Task 2—Non-Linear Systems of Equations 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.

3 years ago
OpenStudy (anonymous):

@phi

3 years ago
OpenStudy (phi):

How far did you get ?

3 years ago
OpenStudy (anonymous):

Not far, I don't understand it.

3 years ago
OpenStudy (anonymous):

f(x) = 2x + 1 y = x^2 + x - 2 I could use these two equations.

3 years ago
OpenStudy (phi):

Create a system of equations that means write down some equations (more than 1) one linear equation - that is the equation of a line and one quadratic equation. -- that is the equation of a parabola solve your system -- that means find the points where they line and parabola meet.

3 years ago
OpenStudy (anonymous):

Oh, that makes sense.

3 years ago
OpenStudy (phi):

I would make up equations that have nice answers. (and are easy to plot) first, does your quadratic "factor" ? i.e can you factor x^2 +x-2 ?

3 years ago
OpenStudy (phi):

yes, no or maybe?

3 years ago
OpenStudy (anonymous):

No?

3 years ago
OpenStudy (phi):

it factors \[ x^2 +x-2 =(x+2)(x-1) \] (You can find a nice parabola by starting with the factored form, and then using FOIL to multiply it out) the point is you have a reasonably easy parabola to plot. so we will use it. now let's find where the line meets the parabola. we do that by setting them equal f(x) = 2x + 1 y = x^2 + x - 2 2x+1 = x^2 + x - 2 add -2x - 1 to both sides

3 years ago
OpenStudy (phi):

2x+1 = x^2 + x - 2 add -2x - 1 to both sides the idea is to "move" all the terms to just one side.

3 years ago
OpenStudy (anonymous):

Okay I think I understand.

3 years ago
OpenStudy (phi):

what do you get after adding -2x-1 to both sides?

3 years ago
OpenStudy (anonymous):

-2x-1 = x?

3 years ago
OpenStudy (anonymous):

Hold on a second.

3 years ago
OpenStudy (phi):

2x+1 = x^2 + x - 2 put in -2x -1 on both sides 2x+1 -2x -1 = x^2 + x -2 -2x -1 can you simplify the left side? the left sides has 2x -2x and 1 - 1

3 years ago
OpenStudy (anonymous):

2(x + 1/2)?

3 years ago
OpenStudy (phi):

look just at 2x+1 -2x -1 you can swap the order, so it looks like this 2x - 2x + 1 - 1 what is 1-1 ?

3 years ago
OpenStudy (anonymous):

0

3 years ago
OpenStudy (phi):

notice when you see lots of terms, look for "just the numbers" and add them up (or subtract) now look at the terms with a single x in them 2x - 2x that is 2 x's take away 2 x's how many x's do we now have ?

3 years ago
OpenStudy (anonymous):

2

3 years ago
OpenStudy (phi):

2x - 2x that is 2 x's take away 2 x's

3 years ago
OpenStudy (anonymous):

Don't the lines connect at points (2,5) and (-1,-1)?

3 years ago
OpenStudy (phi):

not for this line. but we can tweak it. meanwhile, do you have the energy to finish this ?

3 years ago
OpenStudy (anonymous):

Yes, I need to get this done.

3 years ago
OpenStudy (phi):

ok, can you simplify 2x - 2x ?

3 years ago
OpenStudy (anonymous):

x^2

3 years ago
OpenStudy (anonymous):

or 0

3 years ago
OpenStudy (phi):

x^2 means x*x you have 2 x's take away 2 x's (it works the same as 2 spoons take away 2 spoons, or 2 horses take away 2 horses) you get 0 spoons, 0 horses, and 0 x's

3 years ago
OpenStudy (phi):

remember we set the equations equal \[ 2x+1 -2x -1 = x^2 + x -2 -2x -1 \\ 0 = x^2 + x -2 -2x -1 \] now try to simplify the right side. First do the pure numbers.

3 years ago