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| Math Central | Quandaries & Queries |
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Question from benjamin, a student: hi math central. benjamin here. during class, i had problem with this topic. normally i wont have problems with math but this topic i just too hard for me. please help i am having exam and test next week on this topic here is the question: (x-2)/(y-1)=1/3 |
Hi Benjamin,
I want to illustrate with a different question.
using substitution method, solve the simultaneous equation.
$(y+6)/(x-2)=\frac12$$(x-4)/(y+7)=4$
I would first multiply both sides of the first equation by $x-2$ to get
\[y + 6 = \frac12 x - 1.\]
Solving for $y$ gives
\[y = \frac12 x - 7.\]
Substitute this value for $y$ into the second equation to get
\[\frac{x - 4}{\frac12 x - 7 + 7}=4.\]
Solve for $x.$
Cautionary note:
Make sure you verify your answer. For example in my problem we cannot have $x = 2$ or $y = -7$ or at least one of the original fractions would have a denominator of zero.
Penny
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