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## All Questions

#### Q7.    Solve the following pair of linear equations:                (v)

Given Equations,

As we can see by adding and subtracting both equations we can make our equations simple to solve.

So,

Adding (1) and )2) we get,

Subtracting (2) from (1) we get,

Now, Adding (3) and (4) we get,

Putting this value in (3)

Hence,

.

#### Q7.    Solve the following pair of linear equations:                (iv)

Given,

And

Now, Subtracting (1) from (2), we get

Substituting this in (1), we get,

.

Hence,

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#### Q7.    Solve the following pair of linear equations:                (iii)

Given equation,

Now By Cross multiplication method,

#### Q7.    Solve the following pair of linear equations:                (ii)

Given Two equations,

Now By Cross multiplication method,

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#### Q7.    Solve the following pair of linear equations:                (i)

Given Equations,

Now By Cross multiplication method,

#### Q8.    ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral.

As we know that in a quadrilateral the sum of opposite angles is 180 degree.

So, From Here,

Also,

Multiplying (1) by 3 we get,

Now,

Subtracting, (2) from (3) we get,

Substituting this value in (1) we get,

Hence four angles of a quadrilateral are :

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#### Q6.    Draw the graphs of the equations and . Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

Given two equations,

And

Points(x,y) which satisfies equation (1) are:

 X 0 1 5 Y -5 0 20

Points(x,y) which satisfies equation (1) are:

 X 0 1 2 Y -3 0 3

GRAPH:

As we can see from the graph, the three points of the triangle are, (0,-3),(0,-5) and (1,0).

#### Q5.    In a , . Find the three angles.

Given,

Also, As we know that the sum of angles of a triangle is 180, so

Now From (1) we have

Putting this value in (2) we have

Putting this in (3)

And

Hence three angles of triangles

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#### Q3. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Let the speed of the train be v km/h, the time taken by train to travel the given distance be t hours and the distance to travel be d km.

Now, as we Know,

Now, according to the question,

Now, using equation (1), we have

Also,

Adding equations (2) and (3), we obtain:

Substituting the value of x in equation (2), we obtain:

Putting this value in (1), we get:

Hence, the distance covered by train is 600km.

#### Q4.    The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

Let the number of rows be x and number of students in a row be y.
Total number of students in the class = Number of rows * Number of students in a row

Now, According to the question,

Also,

Subtracting equation (2) from (1), we get:

Substituting the value of y in equation (1), we obtain:

Hence,
The number of rows is 4 and Number of students in a row is 9.

Total number of students in a class

:

Hence there is 36 number of students in the class.