Question 12 Marks
Solve the equation $3x + 2 = x - 8$, and represent the solution on: The Cartesian plane.
Answer
On Cartesian plane, equation represents all points on y axis for which $x = -5$ View full question & answer→Question 22 Marks
Find the value of $\lambda$ if $\text{x}=-\lambda$ and $\text{y} = \frac{5}{2}$ is a solution of the equation $x + 4y - 7 = 0$
AnswerWe are given, $x + 4y - 7 = 0 (-\lambda, -5)$ is a solution of equation $3x + 4y = k$
Substituting $\text{x}=-\lambda$ and $\text{y} = \frac{5}{2}$ in $x + 4y - 7 = 0,$
We get; $-\lambda+ 4 \times\Big(\frac{5}{2}\Big) - 7 $
$= 0 -\lambda + 4 \times\frac{5}{2} - 7 = 0$
$\lambda = 10 - 7$
$\lambda = 3$
View full question & answer→Question 32 Marks
The sum of a two digit number and the number obtained by reversing the order of its digits is $121$. lf units and ten's digit of the number are $x$ ard $y$ respectively, then write the linear equation representing the above statement.
AnswerTotal original number is $10y + x$.
The new number is obtained after reversing the order of digits is $10x + y$.
According to question, $(10y + x) + (10x + y) = 121 $
$\Rightarrow 10y + x 10x + y = 121 $
$\Rightarrow 11x + 11y = 121 $
$\Rightarrow x + y = 11$
This is the required linear equation for the given information.
View full question & answer→Question 42 Marks
A number is $27$ more than the number obtained by reversing its digits. If its unit's and ten's digit are $x$ and $y$ respectively, write the linear equation representing the above statement.
AnswerTotal original number is $10y + x$.
The new number is obtained after reversing the order of digits is $10x + y$.
According to question, $10y + x = 10x + y + 27 $
$\Rightarrow 9y - 9x = 27 $
$\Rightarrow y - x = 3 $
$\Rightarrow x - y + 3 = 0$
This is the required linear equation for the given information.
View full question & answer→Question 52 Marks
Check the following are solutions of the equation $2x - y = 6$ and which are not: $(2, -2)$
AnswerWe are given, $2x - y = 6$In the equation $2x - y = 6,$
We have L.H.S $=2 x-y$ and R.H.S $=6$ Substituting $x=2$ and $y=-2$ in $2 x-y$, We get L.H.S $=2 \times 2-(-2)=6 \Rightarrow$ L.H.S $=$ R.H.S $\Rightarrow(2,-2)$ is a solution of $2 x-y=6$.
View full question & answer→Question 62 Marks
Check the following are solutions of the equation $2x - y = 6$ and which are not: $(0, 6)$
AnswerWe are given, $2 x-y=6$ In the equation $2 x-y=6$, We have L.H.S $=2 x-y$ and R.H.S $=6$ Substituting $x=0$ and $y=6$ in $2 x-y$ We get L.H.S $=2 \times 0-6=-6 \Rightarrow$ L.H.S $\neq$ R.H.S $\Rightarrow(0,6)$ is not a solution of $2 x-y=6$.
View full question & answer→Question 72 Marks
If the point $(2, -2)$ lies on the graph of the linear equation $5x + ky = 4$, find the value of $k.$
AnswerIt is given that $(2, -2)$ is a solution of the equation $5x + ky = 4$
$\therefore 5 \times 2 + k \times (-2) = 4$
$\Rightarrow 10 - 2k = 4$
$\Rightarrow -2k = 4 - 10$
$\Rightarrow -2k = -6$
$\Rightarrow\text{k}=\frac{6}{2}$
$\Rightarrow k = 3$
View full question & answer→Question 82 Marks
Check the following are solutions of the equation $2x - y = 6$ and which are not: $(3, 0)$
AnswerWe are given, $2 x-y=6 \ln$ the equation $2 x-y=6$,
We have $L.H.S =2 x-y$ and $R.H.S =6$
Substituting $x=3$ and $y=0$ in $2 x-y$,
We get $L.H.S =2 \times 3-0=6$
$\Rightarrow L.H.S =$
$R.H.S \Rightarrow(3,0)$ is a solution of $2 x-y=6$.
View full question & answer→Question 92 Marks
Check the following are solutions of the equation $2x - y = 6$ and which are not: $\Big(\frac{1}{2},\ -5\Big)$
AnswerWe are given, $2x - y = 6$ In the equation $2x - y = 6$,
We have $L.H.S = 2x - y$ and
$R.H.S = 6$ Substituting $\text{x} = \frac{1}{2}$ and $y =$ in $2x - y,$
we get $L.H.S =2\times\Big(\frac{1}{2}\Big) - (-5)$
$\Rightarrow 1 + 5 = 6 $
$\Rightarrow L.H.S = R.H.S $
$\Rightarrow (12, -5)$ is a solution of $2x - y = 6.$
View full question & answer→Question 102 Marks
Write the equation of a line passing through the point $(3, 5)$ and parallel to $x-$axis.
AnswerWe are given the co-ordinates of the Cartesian plane at $(3, 5).$
For the equation of the line parallel to $x$ axis, we assume the equation as a one variable equation independent of $x$ containing $y$ equal to $5.$
We get the equation as $y = 5$
View full question & answer→Question 112 Marks
Write the equation of a line parallel to $y-$axis and passing through the point $(-3, -7).$
AnswerWe are given the co-ordinates of the Cartesian plane at $(-3, -7).$
For the equation of the line parallel to $y$ axis, we assume the equation as a one variable equation independent of $y$ containing $x$ equal to $-3.$
We get the equation as $x = -3$
View full question & answer→Question 122 Marks
Solve the equation $3x + 2 = x - 8,$ and represent the solution on: The number line.
Answer
$3x + 2 = x - 8$
$\Rightarrow 3x - x = -8 - 2$
$\Rightarrow 2x = -10$
$\Rightarrow x = -5$
Points A represents $-5$ on number line. View full question & answer→Question 132 Marks
A line passes through the point $(-4, 6)$ and is parallel to $x-$axis. Find its equation.
AnswerWe are given the co-ordinates of the Cartesian plane at $(-4, 6).$
For the equation of the line parallel to $x$ axis, we assume the equation as a one variable equation independent of $x$ containing $y$ equal to $6.$
We get the equation as $y = 6$
View full question & answer→Question 142 Marks
If $x = -1, y = 2$ is a solution of the equation $3x + 4y = k$, find the value of $k.$
AnswerWe are given, $3 x+4 y=k$
Given that, $(-1,2)$ is the solution of equation $3 x+4 y=k$.
Substituting $x=-1$ and $y=2$ in $3 x+4 y=k$,
We get; $3 x-1+4 \times 2=k K=-3+8 k=5$
View full question & answer→Question 152 Marks
Plot the points $(3, 5)$ and $(-1, 3)$ on a graph paper an verify that the straight line passing through these points also passes through the point $(1, 4).$
AnswerThe given points on the graph:
It is dear from the graph, the straight line passing through these points also passes through the point $(1, 4).$ View full question & answer→Question 162 Marks
The cost of ball pen is Rs. $5$ less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.
AnswerLet the cost of fountain pen be $y$ and cost of ball pen be $x$. According to the given equation,
we have $\text{x}=\frac{\text{y}}{2}-5$
$\Rightarrow 2x = y - 10 $
$\Rightarrow 2x - y + 10 = 0$
Here y is the cost of one fountain pen and $x$ is that of one ball pen.
View full question & answer→Question 172 Marks
Solve the equation $3x - 2 = 2x + 3$ and represent the solulion on the number line.
AnswerWe are given,
$3x - 2 = 2x + 3$
we get,
$3x - 2x = 3 + 2$
$x = 5$
The representation of the solution on the number line, when given equation is treated as an equation in one variable.
View full question & answer→Question 182 Marks
Check the following are solutions of the equation $2x - y = 6$ and which are not:
$(\sqrt{3}, 0)$
AnswerWe are given, $2 x-y=6$
In the equation $2 x-y=6$,
We have $L.H.S =2 x-y$ and $R.H.S =6$
Substituting $x=\sqrt{3}$ and $y=0$ in $2 x-y$,
We get $L. H. S =2 \times \sqrt{3}-0$
$\Rightarrow$ $L.H.S \neq R.H.S$
$\Rightarrow(\sqrt{3}, 0)$ is not a solution of $2 x-y=6$.
View full question & answer→Question 192 Marks
Write the equation of a line Passing through the point $(0, 4)$ and parallel to $x$-axis.
AnswerWe are given the co-ordinates of the Cartesian plane at $(0, 4).$
For the equation of the line parallel to $x$ axis, we assume the equation as a one variable equation independent of $x$ containing $y$ equal to $4.$
We get the equation as $y = 4$
View full question & answer→