Algebra: Chapter 8, Lesson 3, page 367.
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`
If we line them up, one under the other, we have:
`3x – y = 9`
`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 `x = 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 (multiply) ONE OR BOTH of the equations to make one of the variables disappear. Here is a link that can help!
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 3, Lesson 6, page 139.
Clearing an Equation of Fractions or Decimals
In equations containing fractions, you can use the multiplication property to make the equation easier to solve. To clear the equation of fractions, multiply both sides of the equation by the least common denominator (LCD) of all the fractions in the equation. If you wish to clear the decimals in an equation, multiply both sides by the appropriate power of 10 OR move the decimal places to the left (or right as necessary) for ALL terms an equal amount (e.g., make sure you move them ALL 2 places to the left – obviously, this is the same as multiplying by 100)
Remember the steps to SOLVING EQUATIONS:
- Multiply both sides to clear fractions or decimals, if necessary.
- Collect like terms on each side, if necessary.
- Use the addition property to move the variable to one side and all other terms to the other side of the equation.
- Collect like terms again, if necessary
- Add or subtract to isolate the variable and finally
- Use the multiplication or division or reciprocal properties to solve for the variable.
Two of tonight’s homework problems solved by MrE are here! Just click it and here!