what is x/5 + y/5=3,3x + y=13 by using substitution method pls. show the solution and checking?

Question

pls.......................... :D

Answer 1

okay first take x/5 + y/5 = 3 and times everything by 3 so you have 3x/5 + 3y/5=9 now times everything by 5 so you have 3x + 3y = 45 (notice the 5's on left side cancel when u mulitiply) now take
3x + 3y = 45 and subtract the other equation from it which is 3x + y = 13 so it looks like this
3x + 3y = 45
-3x - y =-13 which gives you
2y = 32 divide by 2 to get
y=16 substitute this value of y in second equation ( 3x + y = 13)
so you have 3x + 16 = 13 subtract 16 from both sides and you will have 3x = -3 divide by there and it gives you x = -1 now plug in both of you values x and y into one of the equations i say the second one because it's much easier but anyways when you plug it in the second one you get 3(-1) + 16 = 13 is this true and the answer is yes therefore it is solved correctly

EDIT: Doin it again with a little more detail for my own sake lol
Equation 1= x/5 + y/5 = 3
Equation 2= 3x + y = 13

(x/5 + y/5 = 3) mulitiply everything in the ( ) by 3
(3x/5 + 3y/5 = 9) multiply everything in the ( ) by 5
3x + 3y = 45 notice the fives on the left side cancel
Now subtract Equation 2 from 3x + 3y = 45
3x + 3y = 45
-3x - y= -13 so this will give you
0x + 2y = 32 divide by 2
y = 16 Substitute your y value into equation 2
3x + y = 13 so you have instead 3x + 16 = 13 subtract 16 from both sides 3x = -3 divide both sides by 3 so you have x = -1 now plug in your x and y values into equation 2
3(-1) + 16 = 13; -3 + 16 = 13; 16 - 3 = 13 which is correct therefore the solutions are correct

Answer 2

x/5 + y/5 = 3

=> x+y = 3 X 5 (taking 5 as L.C.M.)
=> x + y = 15
=> y = 15-x

now substituting y in equation 2

3x + y = 13
=> 3x + (15 - x) = 13
=> 3x +15 - x = 13
=> 2x +15 = 13
=> 2x = 13-15
=> 2x = -2
=> x = -1

now subtituting x in equation 2
3(-1) + y = 13
=> -3 +y = 13
=> y = 13+3
=> y = 16

CHECKING

substituing the values of x and y in equation 2

3(-1) + (16) = 13
-3 +16 = 13
13 = 13

therefore verified


P.S. -{ Thats a good way u have taken out to make other eople do your homework}

Answer 3

x/5+y/5=3
lets solve this first
x+y=15--------------(1)
i got this answer by taking 5 as a common number for x and y and multiplying with 3 with 5.
Then take
3x+y=13-----------(2)
let's calculate both 1 & 2
Im going to multiply 1st formula with 3 so
3x+3y= 45-------------------(3)
3x+y = 13-------------------(4)
Subtract the formula 3 &4. After subtracting it gives as
0x+2y=32
2y=32
y=16; So we got the value of 'y' as 16. Now to get the value of x substitute in the 1st formula
x+y=15,
x+16=15,
x=15-16,
x=-1.

Now substitute the values of x and y in the first and second formulas

Formula (1) x+y=15
-1+16=15;
15=15 thus proved for the 1st formula

Formula (2) 3x+y=13
3(-1)+16=13,
-3+16=13;
13=13

Thus proved

Hope I answered the question ;)

Musthafa

Answer 4

3x + y=13
y = 13 - 3x
x/5 + y/5=3
x/5 + (13 - 3x )/5=3
(x+13-3x)/5=3
(13-2x)=15
15-13= -2x
x= -1,y=10

Answer 5

first we substitute the eq.
let x/5 + y/5 =3 be..............eq.A
let 3x + y =13 be..............eq.B
taking LCM of eq.A
(x+y)/5=3
or x+y=15
or y=15-x........eqC
put value of y in eq B

3x+(15-x)=13
or 3x + 15 - x =13
or 2x=13-15
or 2x=-2
or x= -1.
put x=-1 in eq C
y=15-(-1)
or y=15+1
or y=16..
Verification:

put x=-1 and y=16 in eqA
-1/5 + 16/5 = 3
or (-1+16)/5=3
or 15/5=3
or 3 =3
since boyh sides come out to be the same therefore our answer is correct.
when verifying we must take LHS and RHS seperately

Answer 6

x\5+y\5 =3
then x+y\5=3
then x+y=15
then y=15-x (1)
the other formula
3x+y=13 (2)
from 1 and 2
then 3x+15-x=13
2x=-2
x= -1
from 1
so y =16

Answer 7

x/5+y/5=3
x+y=13

Dist. Prop.:
(x+y)/5=3
(x+y)/5*5=3*5
x+y=15
WHAT?

The equations are impossible. :(

Answer 8

(x/5) + (y/5) = 3
3x + y = 13

(x/5) + (y/5) = 3
x + y = 15
y = -x + 15

3x + y = 13
3x + (-x + 15) = 13
3x - x + 15 = 13
2x + 15 = 13
2x = -2
x = -1

y = -x + 15
y = -(-1) + 15
y = 1 + 15
y = 16

x = -1 and y = 16

Answer 9

multiply 1st eqn by 5,n then subtract it from the 2nd one.
hence u'll get '2x=10'.
hence, x=10/2
hence x=5.
now put x=5 in eqn no.2, n u'll get the value for y.
ie, y= (-2)

Answer 10

Lots of right answers but bob_siso's is by far the most straight forward.