If 3x - 5y = 5 and x/x+y = 5/7 then what is the value of x-y
Answers
Answer:
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Step-by-step explanation:
3x - 5y = 5
x/x + y = 5/7
Don’t simplify x/x to 1 yet; We don’t know if it is 0.
So we start with Eq. 1
3x - 5y = 5
Subtract 3x from all sides
-5y = -3x + 5
Multiply all sides by -1
5y = 3x - 5
Divide all sides by 5
y = 0.6x - 1
Substitute y for 0.6x - 1 in equation 2
x/x + 0.6x - 1 = 5/7
Add 1 to both sides
x/x + 0.6x = 12/7
Convert to fractions
x/x + 3/5x = 12/7
Now we simplify x/x to 1, since x can not be 0, since the answer isn’t 0.
1 + 3/5x = 12/7
Subtract 1 from both sides
3/5x = 5/7
Multiply all sides by 5
3x = 25/7
Divide all sides by 3
x = 25/(7*3)
Simplify
x = 25/21
Find the real y value by substituting x for 25/21 in equation 1
3(25/21) - 5y = 5
Multiply
75/21 - 5y = 5
Simplify once
25/7 - 5y = 5
// 7 is prime, it can not be simplified.
Convert 25/7 to a mixed number
(3 + 3/7) - 5y = 5
Subtract 3+3/7 from all sides
-5y = (1 + 4/7)
Multiply all sides by -1
5y = -(1 + 4/7)
Divide all sides by 5;
Rejoin the mixed number
5y = -11/7
y = -11/(7*5)
Multiply
y = -11/35
Now for x-y…
x = 25/21
y = -11/35
25/21 - (-11/35)
Minus-Minus rule
25/21 + 11/35
LCM of 21 and 35; 105
Adjust denominators
(25*5/21*5) + (11*3/35*3)
Multiply
125/105 + 33/105
Add the numerators
158/105
Given : 3x-5y=5
x/x+y = 5/7
To find : Value of x- y
Solution:
we have,
3x- 5y=5 (1)
x/x+y =5/7 (2)
Using equations we find values of x and y :
x/ x+y =5/7
=> 7x = 5x +5y
=>7x-5x=5y
we get,
2x= 5y
x= 5y/2 (3)
putting valueof x in equation 1
we get,
3×5y/2 - 5y =5
15y/2 -5y =5
5= (15y -10 y)/2
10= 15y- 10 y
10= 5y
y=2
value of y =2
putting y=2 in equation 3:
x= 5× 2/2
x = 5
Now x-y :
= 5- 2
= 3