   SEARCH HOME Math Central Quandaries & Queries  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: using substitution method, solve the simultaneous equation. (x+1)/(y+2)=0.5 (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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.