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# module 5

### system of equations

How many linear equations are in a system of equations? | Answer: Two or more |

Is an ordered pair of numbers a solution of the system of two equations? | Answer: Yes |

How do you determine if (12,6)an ordered pair, is a solution to the system of equations 2x-3y=6 and x=2y? | Replace x with 12 and y with 6 in both equations. solve the equations. If the solutions are true statements than the ordered pair is a solution of the system. |

solve the following equations to see if (12,6)is a solution to the following system. 2x-3y=6 and x=2y | 2x-3y=6 2(12)-3(6)=6 replace x with 12 and y with 6 24-18=6 solve 6=6 True x=2y Replace x with 12 and y with 6 12=2(6) solve 12=12 True |

If an ordered pair is a solution to the system of equations, does the ordered pair have a common point to the graphs of both equations? | Yes, The ordered pair will also have a common point on the graphs of the equations. |

The point of intersection gives the solution of the system. How many solutions are there to the system? | Only one solution to the system if the lines of the graph intersect at a point. |

If you have two equations of a system without a given ordered pair, how do you solve? | You need to make a matrix solving for both x and y in order to find the ordered pairs. |

Once you solve for x and y in the equations how do you graph the solution of the system? | Take two ordered pairs from the matrix and graph the lines. The intersecting point of the lines is the solution to the system. |

How do you solve a system of linear equations without graphing? | Each equation must first be written in slope-intercept form (y=mx+b)Then solve the equations. |

Solve for the following system of equations without graphing. 9x+y=4 and -x+7y=-49 | Write both in slope-intercept form y=-9x+4 and 7y=x-49 Then solve for y y=1/7x-7 the two equations are y=-9x +4 and y=1/7x-7 |

In the equations y=-9x+4 and y=1/7x-7 how many solutions to the system? | There is only one solution since the slopes and the y-intercepts are different. This tells us that the equations are lines intersecting at a single point which can have only one solution |

In the equations y=1/2x-2 and y=1/2x-5/2 how many solutions to the system if the slopes are the same? | There is no solution to the system, since the slopes are the same and the y-intercept is different this tells us that the lines are parallel. |

In the equations y-3x=2 and -6x+2y=4 how many solutions to the system? | put the equations in slope-intercept form which are y=3x+2 and 2y=6x+y(solve for y) This gives the equation y=3x+2 since the slope and y-intercept are the same in both equations the lines of the graph are identical, there are infinitely many solutions. |

Solving linear equations by substitution is more accurate than graphing the solution? | Yes, especially if fractions are involved which are hard to graph accurately. |

What is the first step to solving a linear equation by substitution? | First you need an equation solved for one of its variables either x or y, If neither equation is solved for x or y, this will be your first step. |

Solve for x in the linear equation x+2y=7 of the equations in the system of x+2y=7 and 2x+2y=13 | solve for x by getting the x variable on the left side of the equation by itself. Do this by subtracting 2y from both sides of the equation. The answer is x=7-2y |

What is the second step to solving the system of x+2y=7 and 2x+2y=13 by substitution? | You solved for x which is x=7-2y Second step is to substitute x with 7-2y in the second equation of 2x+2y=13. The answer is y= 1/2 |

What is the third step to solving the system of x+2y=7 and 2x+2y=13 by substitution? | The third step is solving for x. You substitute y=1/2 in the equation x=7-2y. x=7-2(1/2) which equals x=6 you now have the ordered pair (6,1/2) which is the solution to the system of equations of x+2y=7 and 2x+2y=13 |

If solving a linear equation with substitution and one of the variables is already solved such as x=y+2, do I have to solve for one of the variable's as the first step? | No, simply substitute the x variable with y+2 in the other equation. |

How do I check to see if my solutions are correct? | by replacing the ordered pair into the two original equations. |

Created by:
cleann