Solve the following pair of linear equations: | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $u = \frac{1}{x-1}$ and $v = \frac{1}{y-2}$.Substituting these into the given equations,we get:$5u + v = 2$  --- $(1)$$6u - 3v = 1$ --- $(2)$M

Vedclass · Accepted Answer

$x = 4, y = 5$

Vedclass · Answer

(A) Let $u = \frac{1}{x-1}$ and $v = \frac{1}{y-2}$.Substituting these into the given equations,we get:$5u + v = 2$  --- $(1)$$6u - 3v = 1$ --- $(2)$Multiply equation $(1)$ by $3$ to eliminate $v$:$15u + 3v = 6$ --- $(3)$Adding equation $(2)$ and $(3)$:$(6u - 3v) + (15u + 3v) = 1 + 6$$21u = 7$$u = \frac{7}{21} = \frac{1}{3}$Substitute $u = \frac{1}{3}$ into equation $(1)$:$5(\frac{1}{3}) + v = 2$$v = 2 - \frac{5}{3} = \frac{6-5}{3} = \frac{1}{3}$Now,solve for $x$ and $y$:$\frac{1}{x-1} = \frac{1}{3} \implies x-1 = 3 \implies x = 4$$\frac{1}{y-2} = \frac{1}{3} \implies y-2 = 3 \implies y = 5$Thus,the solution is $(x, y) = (4, 5)$.

Solve the following pair of linear equations: $\frac{5}{x-1} + \frac{1}{y-2} = 2$ and $\frac{6}{x-1} - \frac{3}{y-2} = 1$.

Similar Questions

The sum of the digits of a two-digit number is $6$. The number obtained by interchanging the digits is $18$ less than the original number. Find the original number.

$A$ boat goes $32 \, km$ upstream and $36 \, km$ downstream in $7$ hours. In $9$ hours,it can go $40 \, km$ upstream and $48 \, km$ downstream. Determine the speed of the stream and that of the boat in still water. (Speed of boat in still water is more than the speed of the stream of river.)

In $\Delta ABC$,$m \angle A = x$,$m \angle B = 3x$,and $m \angle C = y$. If $3y - 5x = 30$,show that the triangle is right-angled and find the measures of all three angles.

If $(1, y)$ is the solution of the linear equation of two variables $2x + 3y = 8$,then $y = \ldots$

By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them.
$3x + y + 4 = 0$
$6x - 2y + 4 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module