Math Problem Statement

What is the value of the expression below when x, equals, 3x=3 and y, equals, 2y=2? 6, x, minus, y 6x−y

Solution

To solve the expression 6xy6x - y, we first determine the values of xx and yy from the equations:

  1. Given equations:

    • 3x=33x = 3
    • 2y=22y = 2
  2. Solve for xx: 3x=3x=33=13x = 3 \quad \Rightarrow \quad x = \frac{3}{3} = 1

  3. Solve for yy: 2y=2y=22=12y = 2 \quad \Rightarrow \quad y = \frac{2}{2} = 1

  4. Substitute x=1x = 1 and y=1y = 1 into 6xy6x - y: 6xy=6(1)1=61=56x - y = 6(1) - 1 = 6 - 1 = 5

Final Answer:

5\boxed{5}

Would you like a deeper explanation or an alternative method to check this?


Related Questions:

  1. How do you solve linear equations with more variables?
  2. What happens if xx and yy have fractional or negative values?
  3. How would the result change if the coefficients in 6xy6x - y were altered?
  4. Can you graph 6xy6x - y to visualize the result?
  5. What is the significance of expressions in algebraic equations?

Tip:

Always substitute values step by step to avoid calculation errors!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Substitution

Formulas

Expression evaluation: Substitute variables and simplify

Theorems

Basic properties of equality and arithmetic operations

Suitable Grade Level

Grades 6-8