<PRE><B>Question 203932</B>
In the Addition Method, the two equations are added together to eliminate one of the variables. We try to get the coefficients of one of the variables to be opposites so that addition will eliminate it.
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first problem (36):
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3/7x + 5/9y=27
1/9x + 2/7y=7 
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best way to solve this is to remove the denominators.
you get big numbers but you don&#39;t have to worry about fractions.
multiply both equations by 63 because 63 = 9*7 which makes it divisible by 9 and 7 allowing you to remove all denominators.
they become:
27x + 35y = 27*63
7x + 18y = 7*63
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you need to eliminate one of the variables so you can solve for the other one.
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multiply the first equation by -7 and multiply the second equation by 27 because 7 * 27 = 189 and 27 * 7 = 189 allowing you to eliminate the x.
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-189x - 245y = 11907
189x + 486y = 11907
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add the two equations together to get:
241y = 0
so y = 0
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since y = 0, then solve for x.
you have 27x = 27*63 which makes x = 63
you have 7x = 7*63 which makes x = 63
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looks like x = 63 and y = 0
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plug in your original equations to see if this answer is good.
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3/7x + 5/9y=27 becomes 3/7x = 27 becomes x = 7*27/3 = 63
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1/9x + 2/7y=7  becomes 1/9x = 7 becomes x = 9*7 = 63
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answer checks out.
addition method was used.
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second problem (44):
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3x-2.5y=7.125
2.5x-3y=7.3125 
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multiply first equation by 6 and multiply second equation by -5 because 6 * 2.5 = 15 and 5 * 3 = 15 so the y will cancel out.
you get
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18x - 15y = 7.125*6 = 42.75
-12.5x + 15y = 7.3125*(-5) = 36.5625
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you get
5.5x = 42.75 - 36.5625 = 6.1875
x = 1.125
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substitute in one of the equations to solve for y.
3*1.125 - 2.5y = 7.125
3.375 - 2.5y = 7.125
-2.5y = 7.125 - 3.275 = 3.75
y = -3.75/2.5 = -1.5
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x = 1.125
y = -1.5
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substitute in both equations to see if these values are good.
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3x-2.5y=7.125 becomes 3*1.125 + 2.5*1.5 = 7.125 so this one is good.
2.5x-3y=7.3125 becomes 2.5*1.125 + 3*1.5 = 7.3125 so this one is good also.
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answers are:
x = 1.125
y = -1.5
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