Find the value of (x - y), if7x - 8y = 26 : 4x - 5y = 14
Answers
4x - 5y = 14
Find:- (x - y)
Final answer—> 4
Steps. 7x - 8y = 26
=> 7x = 26+ 8y
=> x = (26 + 8y)/7. ————>Eq.1
Substituting Eq.1 in the Eq. 4x - 5y = 14
=> 4 [(26 + 8y)/7] - 5y = 14
=> 104/7 + 32y/7 - 5y = 14
=> (104 + 32y - 35y)/7 = 14
=> 104 - 3y = 14 x 7
=> 104 - 3y = 98
=> -3y = 98 - 104
=> -3y = -6
=> y = -6/-3
=> y = 2.
Substituting value of ‘y’ in Eq.1
=> x = (26 + 8 x 2)/7
=> x = (26 + 16)/7
=> x = 42/7
=> x = 6.
Substituting values of ‘x’ and ‘y’ in the Eq. ( x - y )
=> 6 - 2
=> 4.
Answer:
The value of (x - y) is 16/5.
Step-by-step explanation:
We can use the method of elimination to solve for x and y in the given system of equations.
First, we can multiply the second equation by 2 to get:
8x - 10y = 28
We can then subtract this equation from the first equation to eliminate y:
7x - 8y - (8x - 10y) = 26 - 28
Simplifying this gives:
-x = -2
So we have:
x = 2
We can then substitute this value of x into either of the original equations to solve for y. Using the second equation, we have:
4(2) - 5y = 14
Simplifying this gives:
-5y = 6
So we have:
y = -6/5
Finally, we can find the value of (x - y) as:
x - y = 2 - (-6/5) = 16/5
Therefore, the value of (x - y) is 16/5.
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