SEALs Web Page of Linear Equations.
Method 1:
LINEAR COMBINATION: First, you write out the equations. Then, line them up as shown and make both equations so if they are added one of them will cancel out the other. Add them and find the variable left. After that, you plug the answer you got for one of the variables into one of the original equations and find the other variable. |
x+2y=6 +-x+4y=6 6y=12 y=2 x+2(2)=6 x+4=6 x=2 |
Method 2:
SUBSTITUTION: First, you write out the equations. Then you set one of them to say that either x= or y=. Here we made it y =. Then you replace in the other equation, the y variable with the equation of y=. After you find out the y variable then you can just plug it into these equation and find the x. Don't forget to check your answers! |
2x+4y=6 and 3x+6y=9 x=-2y+3 3(-2y+3)+2y+3=9 y=-3/4 2x+4*(-3/4)=6 x=9/2 (9/2, -3/4) |
Mehod 3:
GRAPHICALLY: Go to the y= button on your calculator and type in the two equations, such as y=5x+3 and y=2x+5, and then push graph. Then, go to 2nd trace, which is calc, and go to 5, which is intersect. then push enter three times and it will tell you the intersect of the lines. |
Word Problem:
| Two Navy SEALs go on a mission. Master Chief Jones takes 5 magazines of bullets with x amount of bullets in each magazine. He picks up 150 bullets during the mission. Senior Chief Clark takes 8 magazines on the mission. During it, he picks up 75 bullets. How many bullets would there have to be in a magazine for their total number of bullets at the end of the mission be the same? | Let y be the total number of bullets at the end of the mission and x be the total number of bullets in a magazine. By doing that, Master Chief Jones's equation would be y=5x+150. Senior Chief Clark's equation would be y=8x+75. If you use your calculator to plug in the equations, then the number of bullets in a magazine for their total numer of bullets to bee the same will be 25. |
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