If x + y = 12 and 3x - y = 20, find the value of 2x - y
Answer Details
We are given two equations as follows:
x + y = 12 .... (Equation 1)
3x - y = 20 .... (Equation 2)
We need to find the value of 2x - y.
To solve the problem, we can use the method of substitution or elimination. Here, we will use the method of substitution.
From Equation 1, we can write:
y = 12 - x
Substituting this value of y in Equation 2, we get:
3x - (12 - x) = 20
Simplifying the equation, we get:
4x - 12 = 20
Adding 12 to both sides, we get:
4x = 32
Dividing both sides by 4, we get:
x = 8
Now, substituting the value of x in Equation 1, we get:
y = 12 - 8
y = 4
Therefore, we have found the values of x and y as 8 and 4, respectively.
Finally, substituting these values in the expression 2x - y, we get:
2x - y = 2(8) - 4 = 12
Hence, the value of 2x - y is 12.