Given:The linear equation that converts Fahrenheit to Celsius is$F=(\frac{9}{5})C+32$.To do:We have to find the solutions of given questions.Solution:Given, $F=(\frac{9}{5})C+32$(i) To draw the linear equation on a graph by taking Celsius on x-axis and Fahrenheit on y-axis.We know that, To draw a graph of a linear equation in two variables, we ... Read More

Given:Yamini and Fatima, two students of Class IX of a school, together contributed Rs.  100 towards the Prime Minister's Relief Fund to help the earthquake victims.To do:We have to write the linear equation which satisfies the given data.Solution:According to the question, Let Yamini's donation be $Rs.\ x$ and Fathima's donation ... Read More

Given: The point $(3, 4)$ lies on the graph of the equation $3y=ax+7$.To do:We have to find the value of $a$.Solution:According to the question, $(x, y)=(3, 4)$Now, by substituting $(x, y)=(3, 4)$ in the equationWe get,  $3(4)=a(3)+7$This implies, $12=3a+7$$12-7=3a$$5=3a$$3a=5$$a=\frac{5}{3}$Therefore, The value of $a$ is $\frac{5}{3}$.Read More

 Given:The taxi fare in a city is $\ Rs. 8$ for the first kilometre and for the subsequent distance it is $Rs.5\ per\ kilometre$.To do:We have to write the linear equation by taking the distance covered as \( x \mathrm{~km} \) and total fare as \( ₹ y \) and ... Read More

To do: We have to find the equations whose graphs are given in fig $4.6$ and fig $4.6$.Solution:For Fig $4.6$Let us substitute the given points in each of the equations in the options.The given points should satisfy the equation whose graph is given in the figure.Therefore, (i) $(-1, 1)$$y=x$$-1≠1$(ii) $(-1, 1)$$x+y=0$$-1+1=0$$0+0=0$$1-1=0$Therefore, ... Read More

Given:$x=2$, $y=1$ is the solution of the equation $2x+3y=k$.To do:We have to find the value of $k$.Solution:According to the question, $x=2$, $y=1$ is the solution of the equation $2x+3y=k$.Now, Let us substitute $x=2$, $y=1$ in the equation $2x+3y=k$We get, $2(2)+3(1)=k$This implies, $4+3=k$$7=k$Therefore, $k=7$The value of $k$ is $7$.Read More

To do:We have to draw the graph for each of the given linear equations in two variables.Solution:We know that, To draw a graph of a linear equation in two variables, we need at least two solutions to the given equation.(i) To find the solutions to the given equation $x+y=4$.Let us ... Read More

Given: Statements:$(i)$ The cube can cast a shadow in the shape of a rectangle.$(ii)$ The cube can cast a shadow in the shape of a hexagon.To do: To check if the given statements are true or false.Solution: We know that a cube casts a shadow in a square shape when the light ... Read More

Given:The cost of a notebook is twice the cost of a pen.To do:We have to write a linear equation in two variables to represent the given statement.Solution:Let the cost of a notebook be $x$ and of the cost of a pen be $y$.According to the question, The cost of a ... Read More

To do: We have to express the given linear equations in the form $ax+by+c=0$ and indicate the values of $a, b$ and $c$ in each of the given cases.Solution:(i) Given, $2x+3y=9.3\overline{5}$We get, The linear equation in the form $ax+by+c=0$ as, $2x+3y-9.3\overline{5}=0$This implies, $2x+3y+(-9.3\overline{5})=0$Comparing, $2x+3y+(-9.3\overline{5})=0$ with $ax+by+c=0$We get, $a=2$, $b=3$ and$c=-9.3\overline{5}$.(ii) Given, ... Read More