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# Ways to solve Systems of Equations # Ways to solve Systems of Equations
1. Subsitution ## 1. Subsitution
- Here we eliminate a variable by subbing in another variable from another equation - Here we eliminate a variable by subbing in another variable from another equation
- We usually do this method if a variable is easily isolated - We usually do this method if a variable is easily isolated
- Example: - Example:
- ``` - ```
y = x + 10 (1) y = x + 10 (1)
x + y + 34 = 40 (2) x + y + 34 = 40 (2)
``` ```
We can sub (1) into (2) to find ```x```, then you the value of ```x``` we found to solve for ```y``` We can sub (1) into (2) to find ```x```, then you the value of ```x``` we found to solve for ```y```
```x + (x + 10) + 34 = 40``` ```x + (x + 10) + 34 = 40```
```2x + 44 = 40``` ```2x + 44 = 40```
```2x = -4``` ```2x = -4```
```x = -2``` ```x = -2```
Then solve for ```y``` Then solve for ```y```
```y = -2 + 10``` ```y = -2 + 10```
```y = -8``` ```y = -8```
2. Elimination ## 2. Elimination
- Here we eliminate a variable by basically eliminate a variable from an equation - Here we eliminate a variable by basically eliminate a variable from an equation
- We usually use this method first when the variables are not easily isolated, then use subsitution to solve - We usually use this method first when the variables are not easily isolated, then use subsitution to solve
- Example: - Example:
- ``` - ```
2x + 3y = 10 (1) 2x + 3y = 10 (1)
4x + 3y = 14 (2) 4x + 3y = 14 (2)
``` ```
We can then use elimination We can then use elimination
``` ```
4x + 3y = 14 4x + 3y = 14
2x + 3y = 10 2x + 3y = 10
------------ ------------
2x + 0 = 4 2x + 0 = 4
x = 2 x = 2
``` ```
Then sub the value of ```x``` into an original equation and solve for ```y``` Then sub the value of ```x``` into an original equation and solve for ```y```
```2(2) + 3y = 10``` ```2(2) + 3y = 10```
```3y = 6``` ```3y = 6```
```y = 2``` ```y = 2```
3. Graphing ## 3. Graphing
- we can rewrite the equations into ```y-intercept form``` and then graph the lines, and see where the lines intersect (P.O.I), and the P.O.I is the solution - we can rewrite the equations into ```y-intercept form``` and then graph the lines, and see where the lines intersect (P.O.I), and the P.O.I is the solution
## Solving Systems of Linear Inequalities ## Solving Systems of Linear Inequalities
- Find the intersection region as the ```solution```. - Find the intersection region as the ```solution```.