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**Solve Systems of Equations by Elimination**

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**Methods to Solve Systems of Equations:**

Graphing (y = mx + b) Substitution Graphing with x- and y- intercepts. Remember, to Solve a System of Equations, you are finding where the lines INTERSECT.

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**How to solve systems of equations by Elimination:**

This method is used when the equations are in standard form: Ax + By = C Set up the equations so the variables line up. 2x + y = 4 x – y = 2 Notice that the x’s & y’s line up on top of each other. Notice that the “y” terms in both equations are opposites of each other. If we add this system together, the “y” terms will cancel out and we can solve for “x”.

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**How to solve systems of equations by Elimination:**

2x + y = x – y = 2 3x = 6 x = 2 Substitute the “x” value into either equation and solve for “y.” 2x + y = 4 2(2) + y = 4 4 + y = 4 y = 0 Add the equations vertically. Get “x” alone. Divide. This is the first part of the ordered pair for your solution. (2, ___) The solution to the system is (2, 0).

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**Solve the system of equations using the elimination method.**

x + 3y = 2 -x + 2y = 3 5y = 5 y = 1 Substitute the “y” value into either equation and solve for “x.” x + 3y = 2 x + 3(1) = 2 x + 3 = 2 x = -1 Add the equations vertically. Get “y” alone. Divide. This is part of the ordered pair for your solution. (___, 1) -1 The solution to the system is (-1, 1).

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**Solve the system of equations using the elimination method.**

2x – y = 2 4x + 3y = 24 In these equations, neither the “x” or the “y” will cancel out, we will have to do an extra step first. THINK of what you can multiply the first equation by so that one of the variables could cancel out. If we multiply the top equation by “3” then the “y”s will cancel out. (3)2x – (3)y = (3)2 6x – 3y = 6 4x + 3y = 24 10x = 30 x = 3 2x – y = 2 2(3) – y = 2 6 – y = 2 -y = -4 y = 4 Now we can add the equations vertically. Divide by “-1” in order to get “y” alone. Get “x” alone. Divide. (3, __) 4 The solution to the system is (3, 4).

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**The solution to the system is (5, -4).**

Solve the system of equations using the elimination method. 4x + 3y = 8 x - 2y = 13 In these equations, neither the “x” or the “y” will cancel out, we will have to do an extra step first. THINK of what you can multiply one of the equations by so that one of the variables could cancel out. If we multiply the bottom equation by “-4” then the “x”s will cancel out. (-4)x – (-4)2y = (-4)13 4x + 3y = x + 8y = -52 11y = -44 y = -4 4x + 3y = 8 4x + 3(-4)= 8 4x – 12 = 8 4x = 20 x = 5 Now we can add the equations vertically. Get “y” alone. Divide. (__, -4) 5 The solution to the system is (5, -4).

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