Name: __________________________________________ Date



Name: __________________________________________ Date: _______________________________

Systems of Equations

|A __________________________________ is a set or collection of equations that you deal with simultaneously. |

|What do solutions to a system look |Graphically: The point (x,y) where the two lines __________________. |

|like? |Algebraically: The point (x,y) that makes both equations __________. |

|Types of Solutions |One Solution |No Solution |Infinite Solution |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

[pic]

Determine if the following ordered pairs are solutions to the system: x - 3y = -5​

-2x + 3y = 10

A. (1,4)

B. (-5,0)

[pic]

Solving Systems by Graphing

|Steps |

|Make sure each equation is in slope-intercept form: y = mx + b. |

|Graph each equation on the same graph paper. |

|The point where the lines intersect is the solution. |

|If they don’t intersect then there’s no solution. |

|Check your solution algebraically! |

1. [pic] 2. [pic]

[pic]

3. [pic] 4. [pic]

[pic]

Solving Systems by Substitution

|Steps |

|One equation will have either x or y by itself, or can be solved for x or y easily. |

|Substitute the expression from Step 1 into the other equation and solve for the other variable. |

|Substitute the value from Step 2 into the equation from Step 1 and solve. |

|Your solution is the ordered pair formed by x & y. |

|Check the solution in each of the original equations. |

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. [pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download