| Recall from the previous page the characteristics of a variable that drops out. On this page, I will show you in these examples how to create the drop out. The basic idea is to select a number to multiply the equation(s) by that will create the needed characteristics. Remember to multiply the ENTIRE equation by the number that you selected. |
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Example # 1
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 5y
- x = 2 |
To make the x drop out, we will multiply
the green equation
by 2. That will make the -x become -2x.
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1
|
 y
+ 2x = 3 |
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Becomes:
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2(5y
- x = 2) |
Use parenthesis around the entire
green equation
to show the multiplication by 2.
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|
1
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y + 2x = 3 |
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Multiply:
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10y
- 2x = 4 |
Use the distributive property on the
green equation.
|
|
1
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y
+ 2x = 3 |
1
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Add them:
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11y = 7
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When you add -2x and +2x, they "drop
out" or sum to zero.
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|
1
|
Notice that X dropped out
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10y + y becomes 11y and 4 + 3 is 7
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Example # 2
|
 7x
- 4y = 3 |
To make the Y drop
out, multiply the red equation by 5
and the blue equation by 4
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|
1
|
3x + 5y = 1 |
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Becomes
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5(7x
- 4y = 3) |
Use parenthesis around
each equation to show this multiplication.
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|
1
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4(3x + 5y = 1) |
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Multiply:
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35x
- 20y = 15 |
The distributive property is used
for each red and
blue
equation.
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1
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12
x + 20y = 4 |
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Add them:
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47x = 19
|
When you add -20y and +20y, they "drop
out" or sum to zero.
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|
1
|
Notice that Y dropped out
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