If 2x + y = 23 and 4x – y = 19; find the value of x – 3y and 5y – 2x

- 20 and 31

Step-by-step explanation:

Solve the given equations simultaneously to find x and y

2x + y = 23 → (1)

4x - y = 19 → (2)

Adding the 2 equations term by term will eliminate y

6x + 0 = 42

6x = 42 ( divide both sides by 6 )

x = 7

Substitute x = 7 into either of the 2 equations and solve for y

Substituting into (1)

2(7) + y = 23

14 + y = 23 ( subtract 14 from both sides )

y = 9

Then

x - 3y = 7 - 3(9) = 7 - 27 = - 20

5y - 2x = 5(9) - 2(7) = 45 - 14 = 31

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.