Question 11 Mark
Find the value of $k,$ if $x = 2, y = 1$ is a solution of the equation $2x + 3y =k.$
AnswerGiven linear equation is
$2x+3y=k$
take $x=2\ \&\ y=1$ then,
$2(2)+3(1)$
$=4+3$
$=7$
so, $k=7$
View full question & answer→Question 21 Mark
Find whether $(1, 1)$ is the solution of the equation $x – 2y = 4$ or not.
AnswerPut $x = 1$ and $y = 1$ in given equation, we get
$x – 2y = 1 – 2(1) = 1 – 2 = –1,$ which is not $4.$
$∴ (1, 1)$ is not a solution of given equation.
View full question & answer→Question 31 Mark
Find whether$(4, 0)$ is the solution of the equation $x – 2y = 4$ or not$?$
Answer$x-2y=4$ Put $x = 4$ and $y = 0$ in given equation, we get
$x – 2y = 4 – 2(0) = 4$
$\therefore (4, 0)$ is a solution of given equation.
View full question & answer→Question 41 Mark
Find whether $(2, 0)$ is the solution of the equation $x – 2y = 4$ or not$?$
Answer$x-2y=4$ Put $x = 2$ and $y = 0$ in given equation, we get
$x – 2y = 2 – 2(0) = 2 – 0 = 2$, which is not $4.$
$\therefore (2, 0)$ is not a solution of given equation.
View full question & answer→Question 51 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $5 = 2x.$
AnswerWe need to express the linear equation $5 = 2x$ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c.$
$5 = 2x{\text{ can also be written as }} - 2x + 0 \cdot y + 5 = 0.$
We need to compare the equation $ - 2x + 0 \cdot y + 5 = 0$ with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c.$
Therefore, we can conclude that $a = - 2,b = 0{\text{ and }}c = 5$
View full question & answer→Question 61 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $y - 2 = 0.$
AnswerWe need to express the linear equation $y - 2 = 0$ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c.$
$y - 2 = 0{\text{ can also be written as }}0 \cdot x + 1 \cdot y - 2 = 0.$
We need to compare the equation $0 \cdot x + 1 \cdot y - 2 = 0$ with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c.$
Therefore, we can conclude that $a = 0,b = 1{\text{ and }}c = - 2$
View full question & answer→Question 71 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $3x + 2 = 0.$
AnswerWe need to express the linear equation $3x + 2 = 0$ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c.$
$3x + 2 = 0{\text{ can also be written as }}3x + 0 \cdot y + 2 = 0.$
We need to compare the equation $3x + 0 \cdot y + 2 = 0$ with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c.$
Therefore, we can conclude that $a = 3,b = 0{\text{ and }}c = 2$
View full question & answer→Question 81 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $2x = -5y.$
AnswerWe need to express the linear equation $2x=-5y$ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c.$
$2x = - 5y{\text{ can also be written as }}2x + 5y + 0 = 0.$
We need to compare the equation $2x + 5y + 0 = 0$ with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c.$
Therefore, we can conclude that $a = 2,b = 5{\text{ and }}c = 0$
View full question & answer→Question 91 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $x = 3y.$
Answer
We need to express the linear equation $x = 3y$ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$
$x = 3y{\text{ can also be written as }}x - 3y + 0 = 0.$
We need to compare the equation $x - 3y + 0 = 0$ with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c.$
Therefore, we can conclude that $a = 1,b = - 3{\text{ and }}c = 0$
View full question & answer→Question 101 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $-2x + 3y = 6.$
AnswerWe need to express the linear equation $ - 2x + 3y = 6$ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c.$
$ - 2x + 3y = 6{\text{ can also be written as }} - 2x + 3y - 6 = 0.$
We need to compare the equation $ - 2x + 3y - 6 = 0$ with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c.$
Therefore, we can conclude that $a = - 2,b = 3{\text{ and }}c = - 6$
View full question & answer→Question 111 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $x - \frac{y}{5} - 10 = 0$
AnswerWe need to express the linear equation $x - \frac{y}{5} - 10 = 0$ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c.x - \frac{y}{5} - 10 = 0{\text{ can also be written as 1}} \cdot x - \frac{y}{5} - 10 = 0.$
We need to compare the equation ${\text{1}} \cdot x - \frac{y}{5} - 10 = 0$ with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c.$
Therefore, we can conclude that $a = 1,b = - \frac{1}{5}{\text{ and }}c = - 10$
View full question & answer→Question 121 Mark
Express the linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in $2x + 3y = 9.3\overline 5$
Answer$2x + 3y = 9.3\overline 5 $
We need to express the linear equation $ 2x + 3y = 9.3\overline 5 $ in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c.$
$2x + 3y = 9.3\overline 5 {\text{ can also be written as }}2x + 3y - 9.3\overline 5 = 0.$
We need to compare the equation $2x + 3y - 9.3\overline 5 = 0$
with the general equation $ax + by + c = 0,$ to get the values of $a, b$ and $c$.
Therefore, we can conclude that $ a = 2,b = 3{\text{ and }}c = - 9.3\overline 5 $
View full question & answer→Question 131 Mark
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
$($Take the cost of a notebook to be $₹\ x$ and that of a pen to be $₹\ y).$
AnswerLet the cost of a notebook be $₹\ x.$
Let the cost of a pen be $₹\ y.$
We need to write a linear equation in two variables to represent the statement, “Cost of a notebook is twice the cost of a pen”.
Therefore, we can conclude that the required statement will be $x = 2y.$
View full question & answer→Question 141 Mark
Give the point $(1, 2),$ find the equation of a line on which it lies. How many such equations are there$?$
AnswerHere $(1, 2)$ is a solution of a linear equation you are looking for. So, you are looking for any line passing through the point $(1, 2).$ One example of such a linear equation is $x + y = 3.$
Others are $y – x = 1, y = 2x,$ since they are also satisfied by the coordinates of the point $(1, 2).$ In fact, there are infinitely many linear equations which are satisfied by the coordinates of the point $(1, 2).$
View full question & answer→Question 151 Mark
Find two solutions for equation: $3y + 4 = 0$
AnswerWriting the equation $3y + 4 = 0$ as $0.x + 3y + 4 = 0,$ you will find that $$$y = -\frac{4}{3}$ for any value of $x.$
Thus, two solutions can be given as $\left(0,-\frac{4}{3}\right) \text { and }\left(1,-\frac{4}{3}\right)$
View full question & answer→Question 161 Mark
Find two solutions for equation: $2x + 5y = 0$
AnswerTaking $x = 0,$ we get $5y = 0$, i.e., $y = 0$. So $(0, 0)$ is a solution of the given equation.
Now, if you take $y = 0,$ you again get $(0, 0)$ as a solution, which is the same as the earlier one.
To get another solution, take $x = 1$, say.
Then you can check that the corresponding value of $y$ is $-\frac{2}{5} \cdot \operatorname{So}\left(1,-\frac{2}{5}\right)$ is another solution of $2x + 5y = 0$
View full question & answer→Question 171 Mark
Find two solutions for equation $4x + 3y = 12$
AnswerTaking $x = 0,$ we get $3y = 12,$ i.e., $y = 4.$
So, $(0, 4)$ is a solution of the given equation.
Similarly, by taking $y = 0,$ we get $x = 3.$
Thus, $(3, 0)$ is also a solution
View full question & answer→Question 181 Mark
Write an equation in two variables: $5y = 2$
Answer$5y = 2$ can be written as $0.x + 5y – 2 = 0$
View full question & answer→Question 191 Mark
Write equation in two variables: $2x = 3$
Answer$2x = 3$ can be written as $2x + 0.y – 3 = 0$
View full question & answer→Question 201 Mark
Write an equation in two variables: $y = 2$
Answer$y = 2$ can be written as $0.x + 1.y = 2,$ or $0.x + 1.y – 2 = 0$
View full question & answer→Question 211 Mark
Write an equation in two variables: $x = –5$
Answer$x = –5$ can be written as $1.x + 0.y = –5,$ or $1.x + 0.y + 5 = 0$
View full question & answer→Question 221 Mark
Write the equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c: 2x = y$
AnswerThe equation $2x = y$ can be written as $2x – y + 0 = 0.$ Here $a = 2, b = –1$ and $c = 0$
View full question & answer→Question 231 Mark
Write the equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c : 4 = 5x – 3y$
AnswerThe equation $4 = 5x – 3y $can be written as $5x – 3y – 4 = 0.$ Here $a = 5, b = –3$ and $c = – 4$
View full question & answer→Question 241 Mark
Write the equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c: x – 4 = \sqrt 3y$
AnswerThe equation $x – 4 = \sqrt 3 y$ can be written as $x – \sqrt3 y – 4 = 0.$
Here $a = 1, b = – \sqrt3$ and $c = – 4$
View full question & answer→Question 251 Mark
Write the equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c : 2x + 3y = 4.37$
AnswerWe have $2x + 3y = 4.37$ can be written as $2x + 3y – 4.37 = 0.$ Here $a = 2, b = 3$ and $c = – 4.37$
View full question & answer→