arc/notes
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

vault backup: 2024-02-02 09:18:16

Browse Source
This commit is contained in:
zleyyij 2024-02-02 09:18:16 -07:00
parent 61c07e2394
commit e2e6c48041
1 changed files with 22 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

22
education/math/Systems of Equations.md
View File

@ -4,3 +4,25 @@
| Inconsistent | Parallel lines, no solution | | Inconsistent | Parallel lines, no solution |
| Independent | The lines only cross at one point. | | Independent | The lines only cross at one point. |
| Dependant | The lines are identical, and there are infinitely many solutions. Both equations represent the same line when plotted. | | Dependant | The lines are identical, and there are infinitely many solutions. Both equations represent the same line when plotted. |
# Solving
## Graphing
Graph the two equations, and look for points where they intersect
## Substitution
Solve for a variable in the equation, then substitute it into another equation.
EG, given the below systems:
$$ y = x+3 $$
$$ x = 3y + 2 $$
You can substitute values, like this:
$$ x = 3(x+3) + 2 $$
Then once you have $x$, you can plug it back into the first equation to solve for y.
## Elimination
To solve a system of equations by elimination, you add the two equations together and see if something cancels out.
A simple example might look like this:
$$ 2x + 3y = 23 $$
$$ 4x -3y = -13 $$
You "add" the two equations together, getting:
$$ 6x + 0y = 10 $$
You now know that $6x = 10$.
If you don't have two values that evenly cancel out, like $3$ and $4$, you can find the least common multiple and multiply the entire equation so that those two are equal. In this case, you'd multiply one equation by 4, and one equation by 3.