Which of these strategies would eliminate a variable in the system of equations?
-7x+2y=5
3x-5y=-5
A. Add the equations
B. Multiply the top equation by 3, multiply the bottom equation by 7, then add the equations
C. Multiply the top equation by 5, multiply the bottom equation by 2, then add the equations.

answer:

-7x+2y=5

-) 3x+5y-=5

——————

5y=-5

y=-5/5

-7x+2(-5/5)=5

24x+2=6

24x=-2

x=-1/12

(-1/12,1/3)

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}