Question

How can you solve the equation 4^x = 2^(x + 2) graphically?

Answer 1

For example:
\[y=4x^{2}-2^{x+2}\]
Just give values to x:
x-----y
-5 ?
-4 ?
-3 ?
.
.
.
.
.
.
.

Answer 2

To solve it GRAPHICALLY, plot the two curves: y = 4^x and y = 2^(x+2). The point(s) where they intersect are the solutions.

Answer 3

what if I said x = 2, based on my calculations, is that neccecary?

Answer 4

This equation is much easier to solve algebraically. yes, x = 2 is the correct answer.
4^x = 2^(x+2)
2^(2x) = 2^(x+2)
2x = x + 2
x = 2.

Answer 5

yeah :)

Answer 6

But they ask you to solve it graphically and so you will have to do it the long way by plotting the two curves.

Answer 7

*2* curves?

Answer 8

Yes. y = 4^x and y = 2^(x+2).
They will intersect at the point (2, 16) and so x = 2 will be the solution.

Answer 9

Yes. If you click on the intersection point it will tell you the coordinates. It will be (2,16).

Answer 10

Ok, thank you
So the answer is:

1. Plot the two equations (y = 4^x and y = 2^(x+2))
2. Find the point where they intersect
3. You will find (2,16)

Answer 11

Because it asks also for steps not just answer

Answer 12

3. You will find the point of intersection is (2,16)
4. Therefore, x = 2 is the solution that satisfies both equations.

Answer 13

Alrighty o'....
Thank you :)

Can you help on another one?

Answer 14

I can try.

Answer 15

An equation is shown below:

9x - y = -2

Part A: Explain how you will show all of the solutions that satisfy this equation. (4 points)

Part B: Determine three different solutions for this equation. (4 points)

Part C: Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent.

I need just C

Answer 16

There are countless answers to C. An easy one could be: 9x - y = 5.
You cannot have a system of 2 equations where 9x - y = -2 AND 9x - y = 5.
The LHS is the same. So for it to be consistent, the RHS has to be the same. Otherwise, the 2 equations will be inconsistent because there is no (x,y) that could satisfy BOTH equations simultaneously.

Answer 17

Oh right, sorry i have made 3 of my own:

9*1-11 where x=1 and y=11
9*2-20 where x=2 and y=20
9*(-1)-(-7)where x=(-1) and y=(-7)

Answer 18

Those are correct answers to Part B.
My answer above is for Part C.
For Part A): 9x - y = -2. Therefore, y = 9x + 2. Pick ANY value for x, and you can find the corresponding y from y = 9x+2.

Answer 19

Can I still use one of my 3 own equations?

Answer 20

Those 3 are NOT equations. You found three SOLUTIONS that satisfy the equation: 9x - y = -2.

For Part C) they are asking you to come up with a NEW EQUATION that is inconsistent with the given equation. One such new equation is: 9x - y = 5.

Answer 21

ok :)
so what do we do next? plug in values in 9x - y = 5?

Answer 22

For Part C) you just say 9x - y = 5 is an equation that is inconsistent with the given equation 9x - y = -2 because these two equations are parallel lines that will never intersect and therefore when you attempt to solve them simultaneously you will find there are no solutions. Therefore, the equations are inconsistent.

Answer 23

Thank you :)

Answer 24

You are welcome.