Question

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.

Answer 1

@phi

Answer 2

How far did you get ?

Answer 3

Not far, I don't understand it.

Answer 4

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

Answer 5

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.

Answer 6

Oh, that makes sense.

Answer 7

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 ?

Answer 8

yes, no or maybe?

Answer 9

No?

Answer 10

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

Answer 11

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

Answer 12

Okay I think I understand.

Answer 13

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

Answer 14

-2x-1 = x?

Answer 15

Hold on a second.

Answer 16

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

Answer 17

2(x + 1/2)?

Answer 18

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 ?

Answer 19

0

Answer 20

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 ?

Answer 21

2

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

Yes, I need to get this done.

Answer 26

ok, can you simplify
2x - 2x ?

Answer 27

x^2

Answer 28

or 0

Answer 29

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

Answer 30

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.