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One day, a long time ago, a little yellow dot by the name of PAC-MAN, set out on a journey to defeat the ghosts haunting his village. As his journey continued, PAC-MAN was ambushed by these ghosts and their powerful leader, The Linear Equation. The Linear Equation wanted to fight PAC-MAN, and as the battle began, PAC-MAN remembered that his friend Dr.PAC told him three different ways to defeat this monster. These are the three methods that PAC-MAN can use to defeat the hated Linear Equation:

SUBSTITUTION:

1.To defeat the Linear Equation by using this method, you must first solve for one of the equations for one of its variables.

2. Next, you must substitute the answer from step 1 into the other equation and solve for the other equation.

3. Finally, substitute the answer from step 2 into the equation used in step 1 and send the final blow into this problem.

EX) 3x + 4y = -4
x +2y = 2

1. x + 2y = 2
x = -2y + 2

2. 3x + 4y = -4
3(-2y + 2) + 4y = -4
y = 5

3. x = -2y + 2
x = -2(5) + 2
x = -8

The solution is (-8,5).

LINEAR COMBINATION:

1. If you want to use this method, first mutiply one or both equations by a constant to obtain coefficients that only differ in sign for one of the variables.

2. Then, add the revised equations from step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable.

3. Now go for the killing blow by substituting the value obtained in step 2 into either of the original equations and solve for the other variable.

EX) 2x - 4y = 13
4x - 5y = 8

1. 2x - 4y = 13 >>>> * -2 >>>>> -4x + 8y = -26
4x - 5y = 8 >>>>>>>>>>>>>> 4x - 5y = 8

2. -4x + 8y = -26
4x - 5y = 8
3y = -18
y = -6

3. 2x - 4y = 13
2x - 4(-6) = 13
x = -11/2

The solution is (-11/2,-6).

GRAPHING:

1. To solve by using the graphing method, fist take the two equations put them into slope-intercept form and graph both of them.

2. Now, all you have to do is find the point of intersection and that ordered pair is your answer.

EX) 2x - 3y = 1
x + y = 3

1. y = (1 - 2x)/-3
y = 3 - x

2. graph into calculater:

The solution is (2,1).

Each tactic that can be used to defeat the Linear Equation works, you must pick which one fits you beast just as PAC-MAN did on that fated day on which he saved his village from destruction.Now you try:

Q. You want to burn 380 calories during 40 minutes of exercise. You burn about 8 calories
per minute inline skating and 12 calories per minute swimming. How long should you spend
doing each activity?

A. First you must shrink the problem down into two equations. In this problem the equations
would be 1. 8x + 12y = 380 and 2. x + y = 40, with x = inline skating and y = swimming.
Now, you must figure out which equation you want to use for this problem. I will use the Linear
Combination method. I will mutiply my 2nd equation by -8 and get -8x - 8y = -320. Then,
add the 1st equation and the revised 2nd equation to get 4y = 60. Solve for y to get y = 15.
Plug in the answer for y into one of the original equations such as x + y = 40 would be
x + 15 = 40, then solve to get x = 25. Therefore, your solution is 25 minutes inline skating and
15 minutes swimming.