$y=11 x-14$
$-11 x+y=[?]$
Answer (1)
Substitute the expression for y from the first equation into the second equation.
Simplify the resulting expression: − 11 x + ( 11 x − 14 ) .
Cancel out the terms − 11 x and + 11 x .
The final answer is − 14 .
Explanation
Understanding the Problem We are given two equations:
Equation 1: y = 11 x − 14 Equation 2: − 11 x + y = [ ?]
Our objective is to find the value of the expression − 11 x + y .
Substitution We can substitute the expression for y from Equation 1 into Equation 2. This means we replace y in the second equation with the expression 11 x − 14 from the first equation.
Performing the Substitution Substituting y = 11 x − 14 into − 11 x + y , we get: − 11 x + ( 11 x − 14 ) Now, we simplify the expression.
Simplifying the Expression Simplifying the expression, we have: − 11 x + 11 x − 14 The terms − 11 x and + 11 x cancel each other out: 0 − 14 = − 14 So, the value of the expression − 11 x + y is − 14 .
Final Answer Therefore, the final answer is − 14 .
Examples
In real-world scenarios, this type of problem can be applied to cost analysis. For example, suppose the cost y to produce x items is given by y = 11 x − 14 , where 11 x represents the cost of materials and labor, and − 14 represents a fixed discount or initial setup cost. If you want to find the difference between the total cost and the material/labor cost (represented by − 11 x + y ), this problem shows that the difference is a fixed value of $-14, which could represent a discount or rebate regardless of the number of items produced.
