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Chapter 2: Problem 50

Find \(y\) given that \(x=3\). $$y-2.895=-1.07(x-2.89)$$

Short Answer

Expert verified
The value of y is 2.7773.

Step by step solution

01

Substitute the Value of x

Given that the value of x is 3, substitute 3 in place of x in the equation: \[ y - 2.895 = -1.07(3 - 2.89) \]
02

Simplify Inside the Parentheses

Calculate the expression inside the parentheses: \[ 3 - 2.89 = 0.11 \] This simplifies the equation to: \[ y - 2.895 = -1.07 \times 0.11 \]
03

Multiply

Multiply -1.07 by 0.11: \[ -1.07 \times 0.11 = -0.1177 \] This further simplifies the equation to: \[ y - 2.895 = -0.1177 \]
04

Solve for y

Add 2.895 to both sides of the equation to isolate y: \[ y - 2.895 + 2.895 = -0.1177 + 2.895 \] This simplifies to: \[ y = 2.7773 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Algebra
Algebra is a branch of mathematics that uses symbols to represent numbers in equations and formulas. These symbols, usually letters like x and y, make it easier to generalize problems and find solutions. In algebra, we often use operations like addition, subtraction, multiplication, and division to solve for unknown variables.
Substitution Method
The substitution method is a technique used to find the value of a variable by substituting known values into an equation. In our exercise, we used substitution to replace x with 3 because we were given that value. Here鈥檚 how it works:
  • Identify the variable to be substituted.
  • Replace that variable with its given or known value.
  • Simplify the equation to solve for the other unknown variable.
This way, it becomes straightforward to pinpoint the unknowns.
Simplification
Simplification involves reducing complex equations or expressions to simpler forms. It makes equations easier to handle and solve. In the given exercise, we simplified inside the parentheses first, calculated the product, and then isolated the variable y. The key steps include:
  • Performing operations inside parentheses first.
  • Combining like terms.
  • Eliminating coefficients by performing inverse operations.
These steps help break down complex problems into manageable parts.
Linear Equations
Linear equations are equations that make a straight line when graphed. They usually have variables raised only to the power of one and can be written in the form: y = mx + b where m represents the slope and b is the y-intercept. In our problem, y - 2.895 = -1.07(x - 2.89), the equation involves simplifying and isolating y to find its value when x is given. Understanding the characteristics of linear equations aids in efficiently solving them.

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