Introduction to Linear Equation in Two Variables

Q. The linear relationship between two variables is called

1. linear expression between two variables
2. quadratic expression between two variables
3. linear equation between two variables
4. quadratic equation between two variables

Q. Initial height of a plant is $50\text{cm}.$ Each day its height increases by $0.5\text{cm}.$ Can the total height of the plant with respect to the days be expressed as a linear equation? If yes, obtain the equation.

1. No. It will not result a linear equation.
2. Yes. The equation is $d=2h,$ where, $h$ is the height in $cm,$ and $d$ is the number of days.
3. Yes. The equation is $2h-d=100,$ where, $h$ is the height in $cm,$ and $d$ is the number of days.
4. Cannot be determined.

Q. Which of the following statement is/are true about linear equation in two variables?

1. One of the variable has exponent as $1.$
2. Both variables have exponent as $1.$
3. They obtain a curve with linearly increasing slope.
4. The graph obtained is a straight line.

Q. A milk vendor mixes water with milk in the ratio of $1:3.$ Obtain the equation that satisfies the above condition.

1. $3y-x=0$
   where, $x$ and $y$ are the quantity of water and milk, respectively.
2. $3y-x=0$
   where, $y$ and $x$ are the quantity of water and milk, respectively.
3. $y-3x=0$
   where, $y$ and $x$ are the quantity of water and milk, respectively.

Q. What will be the relation between $x$ and $y$ based on the data given below in the table?
$x$ value $y$ value

0	1
3	4
6	7
8	9
9	10
11	12

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

Q. Comment regarding solution of a linear equation of two variables.

1. Value of one variable can be known by substituting possible value of the other variable.
2. The solutions are called ordered pairs.
3. They have multiple solutions.

Q. $ax+by=c$ is a standard form of a line. Which of the following statements about this form of line is correct?

1. $x$ and $y$ are variabes
2. $a$, $b$ and $c$ are variables
3. $x$ and $y$ are constants
4. All of the above.

Q.

Write the following as an equation:
$Theproductoftwonumbersisequaltothedifferenceofthosenumbers.$

Q. Coffee $\left(\$x\right)$ and tea $\left(\$y\right)$have a two-dollar difference in prices.
Which of the following equation represents the above statement?

1. $\text{x}-\text{y}=2$
2. $\text{2x}-\text{y}=1$
3. $\text{x}-\text{2y}=1$
4. $\text{x}+\text{y}=-2$