# Jeopardy Systems of Equations

## Solving Word Problems To solve the word problem seen on the far left I started off by underlining all the important information that I was going to need to solve the problem. I then wrote two equations. The first one being x+4y=63 and the second being x+6y=87. I then took the first equation and subtracted 4y from both sides so I could isolate the variable. My equation then became x=-4y+63. I then plugged that whole equation into the second equation making it (-4y+63)+6y=87. After I got that equation I distributed, combined like terms, and then solved. I ended with y=12. Now I had to fine the value of X so I went back to the equation x=-4y+63 and plugged in Y creating the equation x=-4(12)+63. I solved and got x=15. I then plugged by X and Y values back into both of the original equations to check my answers. They work! My coordinate is (15,12). The flat fee is 15 dollars and the additional price per hour is 12 dollars.

## Writing a System To write a system for this problem I broke it down into two equations. 10 gallons of gasoline and 1 quart of oil is equal to 24.50. We do not know the price of a gallon of gasoline or a quart of oil so I represented those price with the variables X and Y. That is how I created my first equation. For my second equations I new that the friends had gotten 8 gallons of gasoline and 2 quarts of oil and it was equivalent to 22 dollars. I then represented the unknown prices as X and Y and that's how I got my second equation. Here I have two equations. Since I am trying to graph them I am going to convert them both into slope intercept form. I am then graphing them onto a graph. Were the points intersect is the answer. This intersection point is (-7,4) and that's the answer!

## When is it best to use each system?

It is best to use elimination when the problem is well dressed (meaning the numbers already cancel out). For example if your systems of equations is -3x+8y=9 and 3x+10=-3 that is best for elimination because the X values already cancel out.

It is best to use substitution when you already given the equations for one of the variables. For example if you are given 8y + 7x = 20 and x=78 it is easy cause you can plug x in to the first equation to find the answer.

It is best too write a system if you are given a word problem but not equations. This will help you find your answer in a non-confusing way. For example the problem "A piggy bank consists of 130 nickels and pennies. The total value of the coins is \$5.10. How many of each were in the piggy bank?" is best fit for writing a system because it does not have one.

It is best to use graphing when the equations are in slope intercept form. Slope-intercept form is easy to graph. For example if your equations are y= 1/5x + 6 and y=6x+8 then this method is best

## What are the three different types of solutions that can arise when solving a System of Equations?

The three different types of solutions that can arise when solving a System of Equations is one solution (having one definite solution), having no solution (no answer can satisfy both equations), and infinite solutions (every number will satisfy this equation).

Examples of one solution- (4,5) (6,19) (20,2) (67,10000) (1,2)
Examples of no solution- 5=6 7=8 67=2
Examples of infinite solutions- 0=0 9=9 1000=1000