If 7x + y = 25 and 6x + y = 23 , what is the value of x?
Answers
x = 2
y = 9
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The value of x is 2.
Given: The equations 7x + y = 25 and 6x + y = 23.
To Find: The value of x.
Solution:
- Whenever we are given a two-equation and we are required to solve it, we shall do so to obtain the values of two unknown variables.
- We can solve such a pair of equations by substitution method or elimination method.
- In this numerical, we shall use the substitution method to find the value of x and y.
- In the substitution method, we shall find an expression in the form of x from the first equation and put it in the second equation to calculate the value of 'y'. Again we shall put this value of y in any of the equations to find the value of 'x'.
Coming to the numerical, we are given;
The equations:
7x + y = 25 ...(1)
6x + y = 23 ...(2)
From (1), we shall make x as the subject;
7x + y = 25
⇒ 7x = 25 - y
⇒ x = ( 25 - y ) / 7 ...(3)
Putting (3), in (2) we get;
6x + y = 23
⇒ 6 × [ ( 25 - y ) / 7 ] + y = 23
⇒ [( 150 - 6y ) / 7 ] + y = 23
⇒ ( 150 - 6y + 7y ) = 23 × 7
⇒ y = 161 - 150
⇒ y = 11
Putting y = 11 in (1), we get;
7x + y = 25
⇒ 7x + 11 = 25
⇒ 7x = 25 - 11
⇒ x = 14 / 7
⇒ x = 2
Hence, the value of x is 2.
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