Recall that variables represent changing values. In this unit, you will work with equations that contain two different variables. What types of situations might be
modeled with equations containing two or more variables? If the value of one variable
changes, must the value of the other variable change for the equation to remain true?
How would the number of solutions for an equation with two variables differ from the
number of solutions for an equation with only one? Explain

It depends on the equations and the variables.

Example of an equation in 2 variables with infinitely many solutions:

sin2x - cos2y + cos2x - sin2y = 0

Example of an equation in 1 variable with 2 solutions:

(x - 1)(x - 2) = 0

Example of 2 equations in 2 variables with no solution:

The intersection of the lines given by

y = 3x + 1

y = 3x + 2

Example of an equation in 1 variable with 1 solution:

5x - 4 = 15

Example of an equation in 1 variable with no real solution:

x2 + 49 = 0

We can go on and on with examples like this. The question is way too general.

Step-by-step explanation:

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geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}