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Syllabus

The taxi fare in a city is as follows: For the first kilometer, the fare is Rs. 8 and for

the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km

and total fare as Rs. y, writes a linear equation for this information

Answer the questions now -

There are two formulae you can use to calculate the number of apple trees and the number of conifer

trees for the pattern described on the previous page:

Number of apple trees = n2

Number of conifer trees = 8n

where n is the number of rows of apple trees.

There is a value of n for which the number of apple trees equals the number of conifer trees. Find the

value of n and show your method of calculating this.

Draw the graphs of the equations x + y = 6 and 2x + 3y = 16 on the same graph paper. Find the coordinates of the points where the two lines intersect

Find four different solutions of the equation 4x+ 5y= 20.The given linear equation in two variables is 4

x+ 5y= 20.We can obtain the solution of the equation by substituting the value of one variable and obtaining the value of the other variable.

If we take

x= 0, we obtain4 × 0 + 5

y= 20,5

y= 20or

y= 4Therefore, (0, 4) is a solution of the given equation.

Now, taking

y= 0, we obtain4

x+ 5 × 0 = 204

x= 20x= 5Therefore, (5, 0) is a solution of the given equation.

Now after this how do you solved the next step. Please expalin in simple wordsa railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. one reserved first class ticket from mumbai to ahmedabad costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. what is the basic first class full fare and what is the reservation charge.

if a

^{x }=b , b^{y }=c , c^{z }=a then prove that xyz=1draw the graphs of the equations x-y=1 and 2x+y=8.Shade the area bounded by these two lines and y-axis.Also,determine this area.

Twice the cost of a Table is equal to 5 times the cost of a chair. Write a linear equation in two variables to represent this statement.

express y in the terms of x in equation 2x-3y=12.find the points where the lines represent by the equation cuts x-axis and y-axis

2/x+3/y=2

1/x-1/2y=1/3

the ratio of income of two persons is 9:7 and the ratio of their expenditure is 4:3.if each of them manages to save Rs.2000 per month, find their monthly income.A grocer buys 10 eggs for Rs.8,set up a linear equation with x representing the number of eggs and y representing the total cost in Rs. By reading the graph find :

1.The cost of 15 eggs

2.number of eggs for Rs.16

the parking charges of a car on New Delhi railway station for first 2 hours is Rs 50/- and Rs 10/-for subsequent hours.write down a equation & draw the graph of this data.Read the charges from the graph.

1)for 1 hour 2)for 3 hours 3) for 6 hours

If a room were 2 metre longer and 3 metre broader, its area would have increased by 75 sq.m. If it were 1 metre shorter and 2 metre broader its area would have increased by 16 sq.m. Find its lenghth and breadth.

write the equation of line which is parallel to x-axis and is at a distance of 3 units below origin. also draw its graph.

if x=2y+6,then find the value of

^{x3}-^{8y3-36xy-216}if(2,3) and (4,0) lie on the graph of equation ax+by=1. find the value of a and b and plot the graph of the equation obtained

HALF THE PERIMETER OF A GARDEN, WHOSE LENGTH IS 4m MORE THAN ITS WIDTH IS 36m. FIND THE DIMENSION OF GARDEN.

Draw the graphs of following equations on the same graph sheet:

x-y=0, x+y=0, y+5=0

Also, find the area enclosed between these lines.

if x=-1, and y=2 in a solution of kx+3y=7,find the value k.

give the equations of 2 lines passing through (2,14).how many more such lines are there and why?

a) x axis b) y axis c)both the axes d)None of these

draw the graph of the linear equation 3x +4y =6 .at what points,the graph cut the x-axis and the y-axis.

## Determine by drawing graph whether the pair of linear equation has infinitely many solutions or not y=5 and Y + 3 = 0.

the ratio of girls and boys in a class is 1:3. Set up an equation between students of a class and boys then draw its graph. Also find the number of boys in a class of 40 students from the graph

Find the distance between the graph of the equations x=-4 and x=-1

draw the graph of 2x+y=6 and 2x-y+2=0.shade the regions bounded by these lines at x axis.find the area of shaded region.

The auto fare in a city is as follows -

For the first 4 km the fare is rs30 and for the subsequent distance it is rs5 per km. Taking the distance covered as x km and total fare as rs y. write a linear equation for this information and draw the graph.

Draw the graph of 3x - 2y + 6=0 and x +2y -6 =0 in a graph paper and find the area is the triangle formed by these two lines and the x-axis

Solve the equation 2x+1=x-3, and represent the solution(s) on

i) the number line

ii) the cartesian line

Give the geometric representations of 2

x+ 9 = 0 as an equation(1) in one variable

(2) in two variables

which of the following is a solution of equation x+2y=7

a) x=3,y=5

b) x=3,y=-5

c) x=3,y=2

d) x=0,y=7

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

(i) 2 units (ii) 0 units

"Two years later a father will be 8 years more than three times the age of the son "Taking the present age of father and son as x and y respectively. Write a linear equation for teh above.Find the age of the father when son is 10 years old

if k

^{2}and y=k is a solution of the equation x-5y+6=0.Find the value of k?Express

in terms ofx, given that 3y+ 4x= 6. Check whether the point (3,2) is on the given line.yFor what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution.

Solve for x and y.

35/x+y+14/x-y=1914/x+y+35/x-y=37Two places A and B are 120 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions, they meet in 1 hour and 12 minutes. Find the speed of the cars.

bx + ay = 1+ c

Give the equation of two lines passing through (2,-3). How many more such lines are there and why?

Q-1 On sellinga T.V. at 5% gain and a fridge at 10% gain , a shopkeeper gains Rs 2000.

But if he sells the T.V. at 10% gain and the fridge at 5% loss . He gains Rs 1500 on the transaction .

Find the actual price of T.V and fridge.

write four solutions of 2x+3y=8.

ravish tells his daughter aarushi,seven years ago , i was seven times as old as you were then.also,three years from now , i shall be three times as old as you will be'.if present ages of aarushi and ravish are x and yyearsrespectively,represent this situation algebraically and graphically.

the graph of equation y=mx+c passes through the origin

TRUE OR FALSE with EXPLANATIONDraw the graphs of the following equations on the same graph x=4,x+5=0,y=2,y-1=0

also,find the area enclosed between these lines.

(1)

X=6y

2 men and 5 boys can finish a piece of work in 4 days,while 3 men and 6 boys can finish it in 3 days. find the time taken by one man alone to finish the work and that taken by one boy alone to finish the work.

A LENDING LIBRARY HAS A fixed charge for the first three days and an additional charge for each day there after.arushi paid 27 for a book kept for 7 days. if fixed charges are x and additional charges are y write the linear equation representing the given information and plot the graph for the same.

Yvaries inversely asX. IfXis increased by25%, then the value of percentage change toYis ?give the equation of two lines passing through (-3,4). how many such lines are possible?

In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:

(i) Draw the graph of the linear equation above using Celsius for

x-axis and Fahrenheit fory-axis.(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?

(iii) If the temperature is 95°F, what is the temperature in Celsius?

(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?

(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

1.)The graph of the linear equation 3x-2y=0 passes through the point

a.) (2/3, -2/3)

b.) (2/3, 3/2)

c.) (1/3, 1/2)

Draw the graph of the line 2x+3y=6 on the graph paper.Write the sum of the intercepts cut by this line on two axes.

I need the answer for this quetion:

Give the geometric representation of 2x+9=0 as an equation : a) in one variable b) in two variable .

Shade the triangle formed by the graphs of 2x-y=4 and x+y=2 and the y-axis. Write the vertices of the traingleCan smone plz answer it wid a figure plzA and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. the age of D and C differ by 40 years. find the ages of A and B.

1) " The cost of a notebook is four times cost of a pencil " . Write a linear equation in two variables to represent this statement .

2) " The cost of a book is three times the cost of a pen " . Write a linear equation in two variables to represent the statement.

3) " The cost of a notebook in twice the cost of a pen" . Write a linear equation in two variables to represent this statement . Also state whether for any solutions of this equation can x or y take negative values ?

4) Write the linear equations in two variables in the form ax + by + c = 0 by using the given values of a , b , c.

a) a = 0 , b = -3 , c = 0 b) a = 1/2 , b = -1/3 and c= 1/6

4)

determine the point on graph of linear equation 2x+5y=19, whose ordinate is1 1/2 times its abscissa.

Draw a graph of the equation 6-1.5x=0.

The taxi fare in a city is as follows: For the first kilometre, the fares is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as

xkm and total fare as Rsy, write a linear equation for this information, and draw its graph.express x=3y in the form ax+by+c=0 and indicate the values of a,b and c . write two solution of the equation

if in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 sq. units. if however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. find the area of the rectangle.

where will we use linear eq in 2 variables in our daily life

draw the graph of the equation 3x+2y=12 at what points does the graph cut the x-axis and the y-axis?

draw a graph of the equationshade the triangle formed between the line & axis.2(x+3)-5(y+1)=6Force applied on a body is directly proportional to the acceleration produced in the body.Write an equation to express the situation and plot the graph of the equation taking the constant to be 5 units.

show that the points A(1,2), B(-1,-16) and C(0,-7) lie on the graph of the linear equation y=9x-7.

distance. Taking total distance covered is x km and total fare is Rs y.

a) Write a linear equation for the above situation

b) A man covers a distance of 15 km and gave Rs 150 to the driver.

Driver said ‘it is not the correct amount’ and returned him the balance.

Find the correct amount paid back by the driver.

if the point [3,4] lies on the graph of the equation 3y=ax+7. find the value of a.

Let y varies directly as x. If y = 15 when x = 3, then write a linear equation. What is the value of y when x = 5?

Draw a triangle whose sides are represented by x = 0, y = 0, and x + y = 3

A student answered equation of line 'q' as x + y = 1. Did he answer correctly ? Also, find the area enclosed between lines p, q and r.

The three wheeler scooter charges Rs 10 for the first km & Rs. 4.50 each for every subsequent km. For a distance of x km, an amount of Rs.y is paid. Write linear eqn representing above information?