Solve Literal Equation

Example on how to solving literal equations .

Example 1

If $\dfrac{3y-t}{y+t}=5$, then y=?
  1. $t$
  2. $3t$
  3. $-2t$
  4. $-3t$
  5. $2t$

Solution

This example is about solving literal equations including several variables.

  1. Rewrite the given equation with rational expression on each side as follows

    $\dfrac{3y-t}{y+t}=\dfrac{5}{1}$

  2. We now use the cross product to obtain

    $(3y-t)\cdot 1 = (y+t)\cdot 5$

  3. Expand and group like terms

    $3y-t=5y+5t$

    $3y-5y=5t+t$

    $-2y=6t$

  4. Solve for $y$

    $y=-3t$

    Answer D