Pre-Algebra: Chapter 5-6
Solving Equations with fractions and decimals
Remember to add or subtract from both sides of an equation to isolate the variable to one side and ALL the rational numbers to the other. Whatever, you do to one side, DO IT TO THE OTHER!
Example: 7/6 = m + 5/12
Isolate the m and subtract 5/12 from both side, the equation now looks like: 7/6 – 5/12 = m + 5/12 – 5/12 or
7/6 – 5/12 = m
Find the LCD (in this case 12ths) and convert to 14/12 – 5/12 = m. The final answer is then 14 – 5 or 9/12 = m. Don’t forget to reduce and m = 3/4!
Algebra: Chapter 8-3
Addition and Subtraction for 2 linear equations.
You can add 2 (or subtract) linear equations together so that one of the variables cancels out. An example would be:
3x – y = 9 and
2x + y = 6
Adding them together, we see that the sum looks like 3x + 2x – y + y = 9 + 6
or 5x = 15 and solving for x makes it = 3. If x = 3, then we can plug it into EITHER original equation, I’ll use the second one and we can solve for y.
So. 2x + y = 6 becomes 2*3 + y = 6 or 6 + y = 6 or y = 0. The ordered pair solution is then (3, 0)!
We may sometimes have to scale one of the equations to make one of the variables disappear. Here is a link that can help!