Question

Solve for x and y 6/(x-1) - 3/(y-2) =1 5/(x-1) + 1/(y-2) =2

Answer 1

Answer:

x=4,y=5

hope it helps

Answer 2

   Answer:

   $x = 4$  ; $y = 5$

   Step-by-step explanation:

   The two given equations are:  $\frac{6}{x-1} - \frac{3}{y-2} = 1$    ---$(1)$

                                                       $\frac{5}{x-1} +\frac{1}{y-2} = 2$   ---$(2)$

   Let $\frac{1}{x-1} = a$ and $\frac{1}{y-2}= b$

⇒ $(1)$ now becomes

   $6a-3b = 1$     ---$(3)$

⇒ $(2)$ now becomes

   $5a + b = 2$       ---$(4)$

   From $(4)$ we get

   $b = 2-5a$

   Substituting the value of $b$ from $(4)$ into $(3)$

⇒ $6a -3(2-5a) = 1$

⇒ $6a - 6 + 15a = 1$

⇒ $21a = 7$

⇒ $a = \frac{1}{3}$

   Substituting the value of $a$ into $(4)$

⇒ $5(\frac{1}{3} ) + b = 2$

⇒ $b = 2-\frac{5}{3}$

⇒ $b = \frac{6-5}{3}$

⇒ $b = \frac{1}{3}$

   We know that $\frac{1}{x-1} = a$ and $\frac{1}{y-2}= b$

⇒ $\frac{1}{x-1} = \frac{1}{3}$     ; $\frac{1}{y-2} = \frac{1}{3}$

⇒ $x-1 = 3$   ; $y-2 = 3$

∴ $x = 4$         ; $y = 5$