Solving the Linear Equation 3y - 4 = 6v - 4

Solving Linear Equations

Equation to Solve

  • The equation given is:
    3y−4=6v−43y - 4 = 6v - 4

Steps to Solve the Equation

  1. Isolate Terms Involving Variables

    • To solve for either $y$ or $v$, first, we notice that the equation can be simplified by eliminating the $-4$ on both sides:
      • Add $4$ to both sides of the equation:
        3y−4+4=6v−4+43y - 4 + 4 = 6v - 4 + 4
        This simplifies to:
        3y=6v3y = 6v

  2. Simplify the Equation Further

    • Now, we can see that the equation is linear in terms of $y$ and $v$.
    • We can solve for $y$ in terms of $v$:
      • Divide both sides by $3$:
        y=63vy = \frac{6}{3}v
        Which simplifies to:
        y=2vy = 2v

Solution Set

  • The solution set for the equation is expressed as:
    y=2vy = 2v
    This indicates that for every value of $v$, there is a corresponding value of $y$ that is twice that value.

Conclusion

  • The final relationship between $y$ and $v$ is represented by the equation: y=2vy = 2v. The solution captures all pairs $(y, v)$ such that $y$ is always twice the corresponding value of $v$.