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# Ways to solve Systems of Equations
1. Subsitution
- Here we eliminate a variable by subbing in another variable from another equation
- We usually do this method if a variable is easily isolated
- Example:
- ```
y = x + 10 (1)
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```
```x + (x + 10) + 34 = 40```
```2x + 44 = 40```
```2x = -4```
```x = -2```
Then solve for ```y```
```y = -2 + 10```
```y = -8```
## 1. Subsitution
- Here we eliminate a variable by subbing in another variable from another equation
- We usually do this method if a variable is easily isolated
- Example:
- ```
y = x + 10 (1)
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```
```x + (x + 10) + 34 = 40```
```2x + 44 = 40```
```2x = -4```
```x = -2```
Then solve for ```y```
```y = -2 + 10```
```y = -8```
2. Elimination
- 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
- Example:
- ```
2x + 3y = 10 (1)
4x + 3y = 14 (2)
```
We can then use elimination
```
4x + 3y = 14
2x + 3y = 10
------------
2x + 0 = 4
x = 2
```
Then sub the value of ```x``` into an original equation and solve for ```y```
```2(2) + 3y = 10```
```3y = 6```
```y = 2```
## 2. Elimination
- 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
- Example:
- ```
2x + 3y = 10 (1)
4x + 3y = 14 (2)
```
We can then use elimination
```
4x + 3y = 14
2x + 3y = 10
------------
2x + 0 = 4
x = 2
```
Then sub the value of ```x``` into an original equation and solve for ```y```
```2(2) + 3y = 10```
```3y = 6```
```y = 2```
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
## 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
## Solving Systems of Linear Inequalities
- Find the intersection region as the ```solution```.