1.4+Notes

Goal 1: rewrite equations with more than one variable. Goal 2: rewrite common formulas.

Solve each equation for y:

Example 1: math 4x+8y=16 \\ \\ \mbox{First we subtract $4x$ from both sides} \\ \begin{array}{ccccc} 4x & + & 8y & = & 16 \\ -4x & & & & -4x \\ \end{array} \\ \\ \mbox{This leaves us with } \\ 8y=16-4x \\ \mbox{ or } \\ 8y=-4x+16 \\ \\ \mbox{We now divide both sides by 8} \\ \begin{array}{ccc} \underline{8y} & = & \underline{16-4x} \\ 8 & & 8 \\ \end{array} \\ \\ \mbox{We now have} \\ y= \left \begin{array}{c} \underline{16-4x} \\ 8 \\ \end{array} \right \\ \mbox{or} \\ y= \frac{16}{8} - \frac{4x}{8} \mbox{ which simplifies to } y=2-\frac{1}{2}x math