IF Y=3x-100 and x=50 then the value of y is
The correct answer and explanation is :
To solve the equation ( Y = 3x – 100 ) for ( x = 50 ), we will substitute the value of ( x ) into the equation and calculate the value of ( Y ).
Step 1: Substitute the value of ( x ) into the equation.
The given equation is:
[
Y = 3x – 100
]
Substituting ( x = 50 ) into this equation:
[
Y = 3(50) – 100
]
[
Y = 150 – 100
]
Step 2: Simplify the expression.
Now, simplify the right-hand side:
[
Y = 150 – 100 = 50
]
Thus, the value of ( Y ) when ( x = 50 ) is 50.
Explanation:
This problem involves solving a linear equation in one variable, ( x ). The equation is given as ( Y = 3x – 100 ), where ( Y ) is the dependent variable, and ( x ) is the independent variable.
- The value of ( Y ) depends on the value of ( x ). The equation represents a straight line, where for every unit increase in ( x ), the value of ( Y ) increases by 3 times the value of that increase, then 100 is subtracted.
- When we are asked to find the value of ( Y ) for a given value of ( x ), we simply substitute the given value of ( x ) into the equation and perform the arithmetic operations.
In this case, we are given that ( x = 50 ). By substituting this value into the equation, we first multiply 50 by 3, which gives 150. Then, we subtract 100 from 150, resulting in 50. Therefore, the value of ( Y ) when ( x = 50 ) is ( 50 ).
This shows the fundamental process of solving a linear equation: substitute known values for the variables, perform the operations, and simplify the result to find the unknown variable.