Answer:
Start by choosing two data points. Calculate the difference between the second y value and the first y value. Then divide that by the difference between the second x value and the first x value.
Step-by-step explanation:
Answer:
or ![$ x = 2 $](https://tex.z-dn.net/?f=%24%20x%20%3D%202%20%24)
Step-by-step explanation:
Given:
![$ f(x) = 2x \hspace{5mm} \& \hspace{5mm} g(x) = 2^x $](https://tex.z-dn.net/?f=%24%20f%28x%29%20%3D%202x%20%5Chspace%7B5mm%7D%20%5C%26%20%5Chspace%7B5mm%7D%20g%28x%29%20%3D%202%5Ex%20%24)
We are to find the values of
such that these two functions are equal.
Substitute
.
We get ![$ f(x) = 2(1) = 2 \hspace{5mm} \& \hspace{5mm} g(x) = 2^{(1)} = 2$](https://tex.z-dn.net/?f=%24%20f%28x%29%20%3D%202%281%29%20%3D%202%20%5Chspace%7B5mm%7D%20%5C%26%20%5Chspace%7B5mm%7D%20g%28x%29%20%3D%202%5E%7B%281%29%7D%20%3D%202%24)
Hence for
we have the functions to be equal.
Now for ![$ x = 2 $](https://tex.z-dn.net/?f=%24%20x%20%3D%20%202%20%24)
![$ f(2) = 2(2) = 4 \hspace{5mm} \& \hspace{5mm} g(2) = 2^{(2)} = 4 $](https://tex.z-dn.net/?f=%24%20f%282%29%20%3D%202%282%29%20%3D%204%20%5Chspace%7B5mm%7D%20%5C%26%20%5Chspace%7B5mm%7D%20g%282%29%20%3D%202%5E%7B%282%29%7D%20%3D%204%20%24)
We see the functions are once again equal.
First set up a proportion
240/160 = 320/200
Cross multiply and if the left equals the right it is similar.
![6 = - 4x + y \\ - 5x - y = 21](https://tex.z-dn.net/?f=6%20%3D%20%20-%204x%20%2B%20y%20%5C%5C%20%20-%205x%20-%20y%20%3D%2021)
Solve the first equation for y
![y = 4x + 6 \\ - 5x - y = 21](https://tex.z-dn.net/?f=y%20%3D%204x%20%2B%206%20%5C%5C%20%20-%205x%20-%20y%20%3D%2021)
Substitute the given value of y into the equation -5x-y=21
![- 5x - (4x + 6) = 21](https://tex.z-dn.net/?f=%20-%205x%20-%20%284x%20%20%2B%20%206%29%20%3D%2021)
When there is a - in front of an expression in parentheses, change the sign of each term in the expression
![- 5x - 4x - 6 = 21](https://tex.z-dn.net/?f=%20-%205x%20-%204x%20-%206%20%3D%2021)
Collect like terms
![- 9x - 6 = 21](https://tex.z-dn.net/?f=%20-%209x%20-%206%20%3D%2021)
Move the constant to the right-hand side and change its sign
![- 9x = 21 + 6](https://tex.z-dn.net/?f=%20-%209x%20%3D%2021%20%2B%206)
Add the numbers
![- 9x = 27](https://tex.z-dn.net/?f=%20-%209x%20%3D%2027)
Divide both sides of equation by -3
![x = - 3](https://tex.z-dn.net/?f=x%20%3D%20%20-%203)
Substitute the given value of x into the equation y=4x+6
![y = 4 \times ( - 3) + 6](https://tex.z-dn.net/?f=y%20%3D%204%20%5Ctimes%20%28%20-%203%29%20%2B%206)
Multiply the numbers
![y = - 12 + 6](https://tex.z-dn.net/?f=y%20%3D%20%20-%2012%20%2B%206)
Calculate the difference
![y = - 6](https://tex.z-dn.net/?f=y%20%3D%20%20-%206)
The possible solution of the system is the ordered pair (x,y)
![(x,y)=(-3,-6)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%28-3%2C-6%29)