# Systems of Equations

### Arianna Tejada

## Jeopardy Problems

## Graphing-300 I first converted the two equations from standard form to slope-intercept form. Then I made a small graph with the two lines and the intersection point is (4,0). | ## Graphing-200 I did the same thing for this one, putting the standard form equations into slope-intercept. The solution I got was (-1,3). | ## Substitution-500 I first converted x+4y=10 into slope-intercept form to isolate the x. Then I substituted it into the 3x of the other equation. When the y was isolated, I got 1. Then I substituted the y with 1. The final answer is (6,1) |

## Graphing-300

I first converted the two equations from standard form to slope-intercept form. Then I made a small graph with the two lines and the intersection point is (4,0).

## Graphing-200

I did the same thing for this one, putting the standard form equations into slope-intercept. The solution I got was (-1,3).

## Elimination-500 To cancel out the -3x, I had to convert the 3y=x+5 into standard form and multiply it by -3 to get 3x-9y=-15. The 3x and -3x canceled out and then I just had to solve for y and x. The solution is (16,7). | ## Word Problem-500 In this problem, I had to find the flat fee (x) plus (y) dollars per hour. They gave me the amount of hours, which was 4 and 6, and the total amount of money, 63 dollars and 87 dollars. I used elimination to solve the equation. I had multiply the second equation by -1 to make the equation opposites. My final answer was (15,12). | ## Write a System-500 In this equation, I had to solve for x, which is the cost for 1 gallon of oil. I used the elimination process to solve it. I first eliminated x to get y and then solved for x to get the solution of 2. |

## Elimination-500

To cancel out the -3x, I had to convert the 3y=x+5 into standard form and multiply it by -3 to get 3x-9y=-15. The 3x and -3x canceled out and then I just had to solve for y and x. The solution is (16,7).

## Word Problem-500

In this problem, I had to find the flat fee (x) plus (y) dollars per hour. They gave me the amount of hours, which was 4 and 6, and the total amount of money, 63 dollars and 87 dollars. I used elimination to solve the equation. I had multiply the second equation by -1 to make the equation opposites. My final answer was (15,12).

## Infinitely Many Solutions This is a special case. You can have infinitely many solutions when both equations are the same, which makes them the same line. | ## No Solutions You have no solutions when the equations have the same slope, making them parallel lines. Parallel lines never cross, so they will never have an intersection point, which is the answer to the system of equations. | ## Exactly one Solution You have exactly one solution when the equations have different slopes and different y intercepts. You get only one intersection point. This is typically what you would get when solving a system of equations. |

## Infinitely Many Solutions

This is a special case. You can have infinitely many solutions when both equations are the same, which makes them the same line.

## No Solutions

You have no solutions when the equations have the same slope, making them parallel lines. Parallel lines never cross, so they will never have an intersection point, which is the answer to the system of equations.