Q1. If $2x + 3y = 12$ and $3x - 2y = 5$, then the value of $y$ is:
Q2. If $29x + 31y = 91$ and $31x + 29y = 89$, then the value of $x + y$ is:
Q3. The pair of equations $x = a$ and $y = b$ graphically represents lines which are:
Q4. Assertion (A): The system of equations $x + 2y = 3$ and $2x + 4y = 7$ is inconsistent. Reason (R): A system of linear equations is inconsistent if $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.
Q5. Solve the following pair of linear equations by the elimination method: $3x - 5y - 4 = 0$ $9x = 2y + 7$.
Solve on white paper.
Q6. Solve for $x$ and $y$ using substitution method: $s - t = 3$ $\frac{s}{3} + \frac{t}{2} = 6$.
Q7. Solve for $x$ and $y$: $99x + 101y = 499$ $101x + 99y = 501$.
Q8. Solve the following pair of equations by reducing them to a pair of linear equations: $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2$ $\frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$.
Q9. Solve for $x$ and $y$: $ax + by = a - b$ $bx - ay = a + b$.
Q10. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Q11. Case Study: Number Game
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits.
(i) Form the pair of linear equations representing the situation.
(ii) Find the number.
(iii) If 27 is added to the number, what is the new number obtained?