Pair of Linear Equations in Two Variables — Class 10 Mathematics (Standard) PYQs

Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Use graphical method to solve the system of linear equations : $y = -3$ and $x + 2y = 4$.

Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

If $x = 1$ and $y = 2$ is a solution of the pair of linear equations $2x - 3y + a = 0$ and $2x + 3y - b = 0$, then :

Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of $8\%$ per annum and $9\%$ per annum, respectively. He received ₹$1,860$ as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹$20$ more as annual interest. How much money did he invest in each scheme ?

A bag contains some red and blue balls. Ten percent of the red balls, when added to twenty percent of the blue balls, give a total of $24$. If three times the number of red balls exceeds the number of blue balls by $20$, find the number of red and blue balls.

The line represented by the equation $x - y = 0$ is :

Assertion (A) : The pair of linear equations $px + 3y + 59 = 0$ and $2x + 6y + 118 = 0$ will have infinitely many solutions if $p = 1$.
Reason (R): If the pair of linear equations $px + 3y + 19 = 0$ and $2x + 6y + 157 = 0$ has a unique solution, then $p\ne 1$.

Case Study - 1

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is :