What are the methods of substitution?

-One Equation: is set equal to a variable

Example:

y = 2x + 1

x + 3y = -12

You already have y, plug it back into x + 3y = -12

x + 3(2x + 1) = -12

x + 6x + 3 = -12

7x + 3 = -12

(Subtract 3 from each side)

7x = -15

(Divide by 7)

x = - 2.14

-No Equation: is set equal to a variable

Example:

2x + y = 10

4× + 2y = -3

Subtract 2x from each side of 2x + y = 10, you should get y= -2x + 10. Now that you have found y, substitute y into 4x+ 2y = -3.

4x + 2(-2x + 10) = -3

4x + -4x + 20 = -3

(Subtract 20 from each side)

4x + -4x = -23

(Add 4x and -4x)

0 = -23

No Solution

-Both Equations: are set equal to a variable

Example:

y = x + 5

y = -x + 3

(you already have y so plug it into the other equation to solve for x)

-x + 3 = x + 5

(Add -x on both sides)

3 = 2x + 5

(subtract 5 from both sides)

-2 = 2x

(Divide by 2 on each side)

x = -1

I hope this helped!

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e