Solve each of the following system of equations by substitution!!!

x-5y=-49
y=-2x+1

x = -4, y = 9

or

(-4, 9)

Step-by-step explanation:

x - 5y = -49

y = -2x + 1

substitute y for -2x + 1

x - 5(-2x + 1) = -49

x + 10x - 5 = - 49

add 5 to both sides

x + 10x - 5 + 5 = - 49 + 5

x + 10x = -44

11x = -44

divide both sides by 11

11x/11 = -44/11

x = -4

substitute x for -4 in any of the original equations

y = -2x + 1

y = -2 * -4 + 1

y = 8 + 1

y = 9

x = -4, y = 9 or (-4,9)

Step-by-step explanation:

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}