Question

Please solve this question!​

Answer 1

`\huge\fbox { \: smaller \: no. = 5}\ \\ \huge\fbox { \: bigger \: no. = 8} \:`

Here,We'll assume the smaller no. as x & the bigger one as y

Now,

ATQ,

• 2x+3y=34_______(1)

(sum of two times the smaller number and three times the bigger number is 34.)

• 5x-2y=9_________(2)

(Two times the bigger number is subtracted from the five times the smaller one)

Now,

we'll apply the elimination method to find The value of the variables↷

• 
  `To \: apply \: the \: elimination \: method, \\ we \: will \: equalize \: either \: of \: the \\ \: variable \: in \: these \: equations \\`

Here,

Let's equalize the variable ,'x'

`To \: equalize \: the \: variable,`

`We \: need \: to \: multiply \: the \: first \: equation \\ \: by \: 5 \: and \: the \: second \: one \: by \: 2↴ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:`

`5(2x + 3y = 34) \\ \: \: \: = > 10x + 15y = 170......(3) \\ \\ 2(5x - 2y = 9) \\ = > 10x - 4y = 18 ......(4)\\ \\`

Since Now our variable'x' is equalize in Both of the equations (10x),

We'll subtract the Equation 4 From Equation 3rd so that we can find out the Value of y

`\: \: \: \: \: \: \: 10x + 15y = 170 \\ \: \ - 10x - 4y = 18 \\ \: \: - - - - - - - - \\ 0 + 19y = 152 \\ \: \: \: - - - - - - - - \\ 19y = 152 \\ (19y)/(19) = (152)/(19) \\ \huge\fbox{y = 8}`

Now,

By plugging the Value of y in any of the equation,we can find the Value of x.

Here,

We'll plug the value of y into the equation 2↴

`5x - 2(8) = 9 \\ 5x - 16 = 9 \\ 5x - 16 + 16 = 9 + 16 \\ 5x = 25 \\ (5x)/(5) = (25)/(5) \\ \huge\fbox{x = 5}`

Hence, the Value of the smaller number = 5

and the value of the bigger one = 8

`\small\mid{ \underline{ \overline{ \tt \: －ɪƭ'ꜱ \: ʙᴙᴜᴛᴀʟ \: σʋʇ \: ɦэŗǝ~}} \mid}`

Answer 2

Answer: smaller number = 5, bigger number = 8

Explanation:

Let x represent the smaller number

and y represent the bigger number.

The sum of 2 times the smaller number and 3 times the bigger number is 34.

EQ1: 2x + 3y = 34

Two times the bigger number is subtracted from 5 times the smaller number is 9.

EQ2: 5x - 2y = 9

Solve the system of equations using the Elimination method:

EQ1: 2x + 3y = 34 → 2(2x + 3y = 34) → 4x + 6y = 68

EQ2: 5x - 2y = 9 → 3(5x - 2y = 9 ) → 15x - 6y = 27

19x = 95

÷19 ÷19

x = 5

Substitute x = 5 into either equation to solve for y:

EQ2: 5x - 2y = 9

5(5) - 2y = 9

25 - 2y = 9

-2y = -16

y = 8

The smaller number (x) is 5 and the bigger number (y) is 8.