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# Solve the system of equations by Elimination Method

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Solve each system by the elimination method. Check each solution. See Examples 1 and 2.

1. x + y = 2 3. 2x + y = -5 5. 3x + 2y = 0
2x - y = -5 x - y = 2 -3x - y = 3

2. 3x - y = -12 4. 2x + y = -15 6 . 5x - y = 5
x + y = 4 -x - y = 10 -5x + 2y = 0

Example 1 - Using the Elimination Method
Use the elimination method to solve the system.
x + y = 5
x - y = 3
Each equation in this system is a statement of equality, so the sum of the
left sides equals the sum of the right sides. Adding in this way gives
(x + y) + (x - y) = 5 + 3.

Combine like terms and simplify to get
2x = 8
x = 4 . Divide by 2.
Notice that y has been eliminated. The result, gives the x-value of the
solution of the given system. To find the y-value of the solution, substitute 4
for x in either of the two equations of the system.

Check the solution set found at the side, {(4, 1)}, by substituting 4 for x and
1 for y in both equations of the given system.
Check -
x + y = 5
4 + 1 _ 5
5 = 5 true

x - y = 3
4 - 1 _ 3
3 = 3 true
Since both results are true, the solution set of the system is {(4, 1)}.

Example 2
Solve the system.
y + 11 = 2x
5x = y + 26

Step 1 Rewrite both equations in the form to get the system
-2x + y = -11 Subtract 2x and 11.
5x - y = 26. Subtract y.

Step 2 Because the coefficients of y are 1 and adding will eliminate y.
It is not necessary to multiply either equation by a number.
Step 3 Add the two equations. This time we use vertical addition.

-2x _ y = -11
5x _ y = 26
3x = 15 Add in columns

Step 4 Solve the equation.
3x = 15
X = 5 divide by 3.

Step 5 Find the value of y by substituting 5 for x in either of the original
equations. Choosing the first equation gives
y + 11 = 2x
y + 11 = 2 (5) let x = 5.
y + 11 = 10
y = _1. Subtract 11.