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