solve the following using two variables.?

Question

1.) find two numbers whose difference is 15 and whose sum is 53.
2.) the sum of two integers is 51.the larger integer is 3 more than twice the smaller integer.find the integers.
3.) if the larger of two numbers is subtracted from 6 times the smaller, the result is 20. if twice the larger number is added to 4 times the smaller, the result is 56. find the numbers.

Answer 1

= 2 points for me

Answer 2

1.let x and y the two numbers

x - y =15; x = 15 + y (equation 1)
x + y = 53 (equation 2)

substitute equation 1 to equation 2

15 + y + y = 53
y = 19 (ans)

substitute y to equation 1

x – 19 = 15
x = 34 (ans)

2. let x be the larger integer

x + y = 51 (equation 1)
x = 3 + 2y (equation 2)

substitute equation 2 to equation 1

3 + 2y + y = 51
3y = 48
y = 16 (ans)

substitute y to equation 2

x = 3 + 2(16)
x = 35 (ans)

3. let x be the larger number and y be the smaller number

x – 6y = 20; x = 20 + 6y (equation 1)
2x + 4y = 56

substitute equation 1 to equation 2

2(20 + 6y) + 4y = 56
40 + 12y + 4y = 56
40 +16y = 56
16y = 16
y = 1 ans

substitute y to equation 1

x = 20 + 6(1)
x = 26 ans

Answer 3

Ohh my god it took nearly more than half an hour for me. U made me to waste few office papers. lol
here my solution is

problem:1
x-y = 15 --------(1)
x+y = 53 -------(2)

(1) + (2) => 2x = 68
x = 34

Sub. X=34 in (2)
34 + y = 53
y = 53 - 34
y = 19

Therefore X =34 and Y = 19
the two numbers are(34,19)
---------------------------------------------------------------------------
Problem : 2
X + Y = 51-------(1)
X = 2y + 3-------(2)
Rearranging (2) as
X - 2y = 3-------(3)

(1) x 2 + (3) =>
2x +2y = 102
x -2y = 3
--------------------
3x = 105 => x = 35

Sub X in (1)
35 + y = 51
y = 51 - 35 => y = 16

Therfore x = 35 and y = 16
Hence the integers are (35,16)
---------------------------------------------------------------------------

Problem : 3

x - 6y = 20------(1)
2x + 4y = 56------(2)

(1) x -2 + (2) => -2x + 12y = -40
2x + 4y = 56
-----------------------
16y = 16
y = 1.

sub y= 1 in (1) => x - 6 = 20
x = 20 + 6
x = 26.
Therfore x = 26 and y = 1
Hence the two numbers are (26,1)

-------------------------------------------------------------------------
will I get 10 points for this. hope so.

Answer 4

34 19 2] 35 16 3]16 6

Answer 5

1) If the smaller number is p, the the greater number is p+15, because their difference is 15.
Their sum is 2p+15 and it should be 53.
So 2p + 15 = 53. Then 2p = 38 and p = 19
So the asked numbers are 19 and 34.

The other problems 2 and 3 you can solve in the same style.

Answer 6

Let the 1st no.=x 2nd no.=y
x+y=53(1)
x-y=15(2)
adding (1) &(2)
x+y=53
x-y=15
then
2x=68
x=68/2=34
now,y=53-34=19
therefore x=34 y=19

Answer 7

1.)
x-y = 15
x+y = 53

2x = 68
x = 68/2 = 34
y = 53 - x = 53 - 34 = 19 A:(34,19).

2.)
x+y = 51
y = 2x+3

x+y = 51
2x - y = -3

3x = 48
x = 48/3 = 16
y = 51 - x = 51 - 16 = 35 A:(16,35)

3.)
6x-y = 20
2y+4x = 56

12x-2y = 40
4x+2y = 56

16x = 96
x = 96/16 = 6
y = (56-4x)/2 = (56-24)/2 = 32/2 = 16 A:(6,16)

Answer 8

1)x+y=53;x-y=15
adding the two eqns..2x=68 => x=34
subtracting eqn 2 from 1,2y=38 => y=19
..
2)x be smaller int. 2x+3 is larger int.
so... x+2x+3=51
ans : x=16
.........=>16 and 35
..
3)larger no is y,smaller no is x
y-6x=20 and 2y+4x=56
solving the equations...x=1 and y=26

Answer 9

(1) x=34 ;y=19
(2) x=32 ;y=19
(3) x=2 ;y=-13

Answer 10

1.) x=34, y=19
2.) x=35, y=16
3.) x=26, y=1

x= larger no and y= smaller number

Answer 11

1.) 34 and 19