Question 1 :
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?
Question 2 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are intersecting when _____________.
Question 3 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x – 3y = 8 ; 4x – 6y = 9$
Question 4 :
Use elimination method to find all possible solutions of the following pair of linear equations :$2x + 3y =8 , 4x + 6y =7$
Question 5 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x – 5y – 4 = 0 ~and ~9x = 2y + 7$
Question 6 :
Solve the following pair of linear equations by the substitution method : $x + y = 14 ; x - y = 4$
Question 7 :
Solve, by substitution : $x + 2y – 4 =0 , 2x + 4y – 12 =0$
Question 8 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $x + y = 5 , 2x + 2y = 10$
Question 9 :
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
Question 10 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b5c273b230584979988.png' />
In the above given graph of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0, calculate the area of the triangle formed by the lines so drawn and the x-axis.