Math Problem Statement

Which of the following shows the equation solved for y? 2x + 6y = -12

Solution

To solve the equation 2x+6y=122x + 6y = -12 for yy, let's follow these steps:

  1. Isolate the term with yy:

    Subtract 2x2x from both sides: 6y=2x126y = -2x - 12

  2. Solve for yy:

    Divide every term by 6 to isolate yy: y=2x126y = \frac{-2x - 12}{6}

  3. Simplify the equation:

    Simplify each term: y=2x6126y = \frac{-2x}{6} - \frac{12}{6} y=13x2y = -\frac{1}{3}x - 2

This corresponds to option (b) y=2x2y = -2x - 2, which looks different but is not simplified correctly. The equation obtained is:

y=13x2y = -\frac{1}{3}x - 2

Unfortunately, none of the provided options match exactly after the complete simplification.

Would you like more details on this or further assistance with another problem?


Relative Questions:

  1. What does it mean to "solve for yy" in an equation?
  2. How do you isolate a variable in a linear equation?
  3. How can simplifying fractions in algebraic expressions help solve equations?
  4. Why is it important to check your answer against the original equation?
  5. What is the difference between solving equations in standard form and slope-intercept form?

Tip: Always double-check the options given in multiple-choice questions after solving to ensure proper simplification and matching with choices.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Solving for Variables

Formulas

y = (mx + b)

Theorems

Linear Equation Solving

Suitable Grade Level

Grades 6-8