Question 160159: could you please help me my question is if the two given equations are being solved so that one unkonwn is eliminated by the method of comparison,which of the following steps is essential? 3x + 2y=7 6x -5y =8 A)6x + 4y = 14 6x - 5y = 8 B) 15x = 10y = 35 12x - 10y = 16 C)6x then there is a line that has a 7 - 2y over the top of it and a 3 on the bottom of it then - 5y = 8 sorry i dont know how to set it up right anwser D is 7 -3x over 2 then = 6x over 5 if you could help me that would be great thank you for all you do.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! method of comparison works on the principal if a = b and b = c, then a = c.
that's what i understand from what i read.
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in your equations you have
3*x + 2*y = 7, and
6*x - 5*y = 8
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solving for x in first equation gets x = (7-(2*y))/3
solving for x in the second equation gets x = (8+(5*y))/6
since (7-(2*6))/3 = x and (8+(5*y))/6 = x, then they must equal to each other, so
(7-(2*y))/3 = (8+(5*y))/6
multiplying both sides by 6 to remove denominators gets
6*(7-(2*y))/3 = 6*(8+(5*y))/6 becomes
2*(7-(2*y)) = (8+(5*y)) becomes
14 - 4*y = 8 + 5*y
adding 4*y to both sides of the equation and subtracting 8 from both sides of the equation gets
14 - 8 = 5*y + 4*y becomes
6 = 9*y becomes
y = 6/9
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now that you have y, you substitute in one of the equations to get x.
use the first equation
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3*x + 2*y = 7 becomes
3*x + 2*(6/9) = 7
multiply both sides of equation by 9 to remove denominator.
(3*9*x) + (2*6*9)/9 = 7*9
27*x + 12 = 63
27*x = 51
x = 51/27 = 17/9
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your answer looks like
x = 17/9
y = 6/9
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substituting in first equation gets
3*x + 2*y = 7
3*(17/9) + 2*(6/9) = 7
multiplying both sides of equation by 9 gets
3*17 + 2*6 = 63
51 + 12 = 63
63 = 63
first equation is good.
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substituting in second equation gets
6*x - 5*y = 8
6*(17/9) - 5*(6/9) = 8
multiplying both sides of equation by 9 gets
6*17 - 5*6 = 8*9
102 - 30 = 72
72 = 72
second equation is good.
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