Journey with Jenni Through Equations!
Linear Combinations
| x + 2y = 8
-x + 3y = 7 5y/5 = 15/5 y = 3 x
= 2
|
* The 2 x's cancel
out so you are left with 2y = 8 and 3y = 7.
* When you add these 2 you get 5y = 15, which you cancel out by dividing by 5y on each then you get y = 3. * x + 2(3) = 8 which makes x + 6 = 8 * ? + 6 = 8 or say 8 - 6 = 2 * The answer is y = 3 and x = 2 |
| 4x + y = 8
3x - y = 6 7x/7 = 14/7
|
* The 2 y's cancel
each other out
* You add 4 + 3 which is 7 and 8 + 6, which is 14. * When you divide each by 7x, then the 2 7's cancel out and x becomes 2. * When you put x in the equation, you know right off that y had to be 0. |
The
Substitution Method
| 3x - 2y = 11
y = 5 - 2x 3x - 2(5 - 2x) = 11
7x/7 = 21/7
3(3) - 2y = 11
|
* In the first equation,
you substitute the y in its place because the second equation is equal
to the variable.
* 3x - 2(y=equation) = 11 * You add the 2 x's which becomes 7x * The -10 goes over to the 11 so you add the 2. * The new equation becomes 7x/7 = 21/7 * x = 3 and y = -1 |
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