Solve the following pair of linear equations:
$px + qy = p - q$
$qx - py = p + q$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given equations are:
$px + qy = p - q \quad \dots(1)$
$qx - py = p + q \quad \dots(2)$
To eliminate $y$,multiply equation $(1)$ by $p$ and equation $(2)$ by $q$:
$p(px + qy) = p(p - q) \implies p^2x + pqy = p^2 - pq \quad \dots(3)$
$q(qx - py) = q(p + q) \implies q^2x - pqy = pq + q^2 \quad \dots(4)$
Adding equations $(3)$ and $(4)$:
$(p^2x + pqy) + (q^2x - pqy) = (p^2 - pq) + (pq + q^2)$
$p^2x + q^2x = p^2 + q^2$
$x(p^2 + q^2) = p^2 + q^2$
$x = \frac{p^2 + q^2}{p^2 + q^2} = 1$
Substituting $x = 1$ in equation $(1)$:
$p(1) + qy = p - q$
$p + qy = p - q$
$qy = -q$
$y = -1$
Thus,the solution is $x = 1$ and $y = -1$.

Explore More

Similar Questions

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

From a bus stand in Bangalore,if we buy $2$ tickets to Malleswaram and $3$ tickets to Yeshwanthpur,the total cost is ₹ $46$; but if we buy $3$ tickets to Malleswaram and $5$ tickets to Yeshwanthpur,the total cost is ₹ $74$. Find the fares from the bus stand to Malleswaram and to Yeshwanthpur.

Form the pair of linear equations for the following problem and find their solution by the substitution method.
The difference between two numbers is $26$ and one number is three times the other. Find the numbers.

Form the pair of linear equations for the following problems and find their solution by the substitution method.
The coach of a cricket team buys $7$ bats and $6$ balls for ₹ $3800$. Later,she buys $3$ bats and $5$ balls for ₹ $1750$. Find the cost of each bat and each ball.

Difficult
View Solution

The cost of $2$ pencils and $3$ erasers is ₹ $9$,and the cost of $4$ pencils and $6$ erasers is ₹ $18$. Determine the cost of each pencil and each eraser.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo