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Frame a linear equation in the from \(ax + by + c = 0 \)
(i) \(a = – 2, b = 3, c = 4 \)
(ii) \( a = 5, b = 0, c = 7\)
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(i)
(ii)
Express each of the following equations in the form \(y = mx + c \)
(i) \(3x – y = 4 \)
(ii) \(2y – x = 2 \)
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(i)
(ii)
Draw the graph of the linear equation in two variables : \(2x + y = 3\)
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If ,
If
If
Find the coordinates of points where the graph of equation \(4x + 3y = 12\) intersects xaxis and yaxis.
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Putting in equation
So point intersect xaxis is (3, 0) putting in equation
So point intersect yaxis is (0, 4)
The auto fares in a city are as follows. For the first kilometre the fare is Rs 12 and for the subsequent distance it is Rs 7 per km. Taking the distance covered as x km and the total fare as Rs y, write a linear equation.
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Let the distance be km
Total fare
A/Q
Give geometric representation of equation \(3x + 12 = 0\) in (i) one variable (ii) two variables
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(i) In one veriable, is a point
In two variables
Put
Put
Points are (4, 0) and (4, 1)
After 5 years, the age of father will be two times the age of son. Write a linear equation in two variable to represent this statement
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Let the age of father be and son be
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
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Let the cost of pen and cost of a note book
At what point does the graph of the linear equation \(x + y = 5\) meet a line which is parallel to the yaxis, at a distnace of 2 units from the origin in the positive direction of xaxis ?
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The required point is (2, 3)
Let \(y \) varies directly as \(x \). If \(y=12 \) when \( x=4\) then write a linear equation. What is the value of \(y \) when \(x=5 \) ?
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Determine the point on the graph of the linear equation \(2x + 5y = 19\) whose ordinate is \(1\dfrac{1}{2} \) times of its abscissa.
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Let abscissa be
ordinate
ordinate
Point
Find three solutions of \(5x – y + 6 = 0\) after reducing it to \(y = mx + c\) form.
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The 3 solutions are
Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.
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For , lies on the graph of
For lies on the graph of
Coordinates are
For what value of \(p \), the linear equation \(2x + py = 8\) has equal values of \(x \) and \(y \) for its solution?
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Find any three solutions for the equation \(15x – 2y = 7\).
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Draw the graph 2x + y = 4 and find the area of the triangle formed by the line with xaxis and yaxis.
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Base of the triangle
Height
Area
The cost of a table exceeds the cost of the chair by Rs 150. Write a linear equation in two variables to represent this statement. Also, find two solutions for the same equation.
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Let the cost of table be and chain be
Solve for \( x:x1=\dfrac{3}{4}\ (x+1)+\dfrac{1}{2}\)
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If the number of hours for which a labourer works is x and y are his wages (in rupees) and y = 2x – 1, draw the graph of the workwages equation. From the graph, find the wages of the labourer if he works for 6 hours.
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The time for which a labour works is hours and his wages is
when we have
when we have
when we have
So wages of labour if the works for 6 hour is ₹ 11
Ashish and Deepak contribute to charity. The contribution of Ashish is \(\dfrac{1}{2} \) of contribution of Deepak. Write a linear equation to represent the above and draw the graph. From the graph, find the contribution of Ashish, if Deepak contributes Rs 50.
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Let ashish’s contribution be and deepak’s contribution be
If deepak’s contribution is 50 then ashish’s contribution is
Give geometric representation of \(2y + 7 = 0 \) as an equation :
(i) in one variable
(ii) in two variable
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In one variable
So we can say that in one variable the equation is a point
In two variable,
Points are
Find \(a \), if \(\dfrac{a+3}{a2}=\dfrac{a+2}{a+7}a\ne2,a\ne7 \)
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Sum of the digits of a two digit number is 14. If we add 18 to the original number, the digits interchange their places. Write two equations for these two statements.
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Let the unit digit be and ten’s digit be
original number
A/Q
Also
The food charges in a hostel are as follows : For the first day, the charges are Rs 100 and for the subsequent days it is Rs 50 per day. Taking the number of days as x and total charges as Rs. y, write a linear equation for this information and draw its graph.
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For
Solve for \(\dfrac{7x1}{4}\dfrac{1}{3}\left(2x+\dfrac{x1}{2}\right)=6\dfrac{1}{3} \)
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Draw the graph of two lines, whose equations are 3x – 2y = 4 and x + y – 3 = 0 on the same graph paper and find the coordinates of the point where two lines intersect.
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Let
Intersection is at
Rs 27 is in the form of 50 paise, 25 paise and 20 paise coins. The number of 25 paise coins is double the number of 20 paise coins but half the number of 50 paise coins. Find the number of coins of each type.
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Let the number of 50 paise coins paise coins and 20 paise coins
so,
Solve : \(\dfrac{y3}{5}+\dfrac{y4}{7}=6\left[\dfrac{2y1}{35}\right] \)
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A number consists of 2 digits. The digit at tens place is 2 times the digit in units place. The number formed by reversing the digit is 27 less than the original number. Find the number.
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Let the digit at tens place
unit place
Number
A/Q
Also
Number
A man leaves half his property to his wife, one third of the remaining to his son and the rest to his daughter. If daughter’s share is Rs 15000, how much money did the man leave? How much money did his wife and son each get?
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Let the property be
wife
Son
Daughter
A/Q
wife
Son
You know that the force applied on a body is directly proportional to the acceleration produced in the body. If constant of proportionality is 2, write an equation to express this situation and plot the graph of equation.
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Let the force be and is acceleration
I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. How old am I and how old is my son?
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Let age be years
Son’s age years
My age is 45 years and my son’s age is 15 years
If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is 2 units.
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Let the distance be
work done
The following values of \(x \) and \(y \) are thought to satisfy a linear equation.
Draw the graph, using the values of \(x \) and \(y \). At what points the graph cuts the xaxis and yaxis.
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The graph cuts the xaxis at and yaxis at
A and B are friends. A is elder to B by 5 years. B’s sister C is half the age of B while A’s father D is 8 years older than twice the age of B. If the present age of D is 48 years, find the present ages of A, B and C.
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Let the present age of B be
The present age of A = 20 + 5 = 25 years
The present age of B = 20 years
The present age of C = 10 years
Solve for \(x:\dfrac{3x5}{3}+\dfrac{4x+2}{5}=\dfrac{25x+7}{15} \)
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