Question Text
Question 1 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are coincident lines.
Question 2 :
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 down-stream. Determine the speed of the stream and that of the boat in still water.
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdd273b230584979a31.JPG' />
In the above fig, ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadilateral?
Question 4 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{1}{2x} + \frac{1}{3y} = 2 ; \frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$.
Question 5 :
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Question 6 :
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates ofthe vertices of the triangle formed by these lines and the y axis.
Question 7 :
Other than algebraical methods, how can the pair of linear equations be solved?
Question 8 :
For which values of p and q, will the following pair of linear equations have infinitely many solutions? 4x + 5y = 2 and $\left(2p+7q\right)x+\left(p+8q\right)y=2q-p+1$.
Question 10 :
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
