Algebra: Chapter 8, Lesson 2, page 362.
Substitution Method
You can solve 2 equations by solving 1 equation for 1 variable and then substituting that equivalent expression in the other linear equation. By doing this, you eliminate one variable. Solve for the remaining variable and then substitute its value in the original equation to find the first variable.
Here is an example of 2 equations to solve, its easier that way:
`x – 2y = 6` and `3x + 2y = 4`
1. Solve the first equation for x, so … `x = 6 + 2y` (added `2y` to both sides)
2. substitute for `x` in the second equation which now looks like: `3(6 + 2y) + 2y = 4`.
3. Distribute the new equation in `y`, it now looks like: `18 + 6y + 2y = 4`
4. combining like terms we have: `18 + 8y = 4` or simplifying
`8y = 4 – 18` … or … `8y = -14` and `y` is finally = `-14/8` or we reduce it to `-7/4`!
5. With `y = -7/4`, we can use the first equation to write:
`x – 2(-7/4) = 6` … or …. `x + 7/2 = 6` … or …. `x = 5/2`!
6. The solution is then, `(x,y)` or `(5/2, -7/4)`, wow!!!!
Here are some more examples done by purplemath.com with substitution!
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!