Y+2=3(x-1)y=-2x+10
What is the solution to the system ( , )

(3, 4)

Step-by-step explanation:

y+2=3(x-1)y=-2x+10 should be written as y + 2 = 3(x - 1)      y = -2x + 10 or

y + 2 = 3(x - 1)      

y = -2x + 10

Let's eliminate y temporarily.  Substitute -2x + 10 for y in the first equation, obtaining:

-2x + 10 + 2 = 3x - 3

Now combine the x terms on the right and the constants on the left:

10 + 2 + 3 = 3x + 2x

so that

15 = 5x.  Then x must equal 3.  Using the second equation, we now find y by substituting 3 for x:  

y = -2(3) + 10, or y = 4

The solution to this system is (3, 4)

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}