Forming Linear Equation in two Variables based on Statements

Q.

Write the linear equation such that each point on its graph has an ordinate $3$ times its abscissa.

Q. Father's age is 6 more than thrice the age of son. Convert the statement into linear equation in two variable.

1. $6+3x=y$, where $x$ is age of son and $y$ is age of father.
2. $3y-6=x$, where $x$ is age of son and $y$ is age of father
3. $x+3y=6$ where $x$ is age of son and $y$ is age of father

Q. The difference between a number $x$ and twice of another number $y$ is expressed as $12$. What is this statement's equation form?

1. $x-2y=12$
2. $x+2y=12$
3. $x+2y=6$
4. $2x-y=6$

Q. If Lionel Messi $\left(x\right)$ scores twice as many goals as Cristiano Ronaldo $\left(y\right)$ in a single La Liga season. Which of the following statements is true if both players scored $76$ goals in the same season?

1. $x+y=76$
   $2x=y$
2. $x-y=76$
   $2x=y$
3. $x-y=76$
   $x=2y$
4. $x+y=76$
   $x=2y$

Q. In a class, Number of girls are $\frac{7}{3}$ of number of boys in class. evaluate the equation.

1. $3y=7x$ where number of girls is $y$ and number of boys is $x$
2. $x=\frac{7}{3}y$ where number of girls is $y$ and number of boys is $x$
3. $x+y=\frac{7}{3}$ where number of girls is $y$ and number of boys is $x$
4. $3x-7y=0$ where number of girls is $y$ and number of boys is $x$

Q. A cab driver charges $\$3$ for distance under 5 km and if distance increased by 5 km then for subsequent distance it charges $\$1/\text{km}$.

A person books cab and he travelled $x$ km and pays $\$y$ to cab driver. Formulate this situation in linear equation in two variable.

1. $y=x-2$
2. $y=x-5$
3. $y=11(x-5)$
4. None of the above

Q. A two-digit number is 6 less than $(\frac{3}{5}{)}^{th}$ of number formed by reversing the digits of original number. Form the linear equation in two variable.

1. $47x-25y+30=0$, Where $xy$ is original number.
2. $40x-25y+30=0$, Where $xy$ is original number.
3. $47x-25y+30=0$, Where $yx$ is original number.
4. All of the above.

Q. Cost of textbook is 8 more than one third the cost of notebook.Deduce this statement into linear equation in two variables. Also what will be the cost of notebook when cost of textbook is $\$12$.

1. $x=y+\frac{8}{3}$, Where $x$ is cost of textbook and $y$ is cost of notebook
2. $x=\frac{y}{3}+8$, Where $x$ is cost of textbook and $y$ is cost of notebook
3. Cost of notebook will be $\$12$
4. Cost of notebook will be $\$10$