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QUESTION: 1

If a pair of linear equations has infinitely many solutions, then the lines representing them will be

Solution:

If two lines are coincident then, they have infinite solution and a pair of linear equations is consistent; If two lines are intersecting then, they have a unique solution and a pair of linear equations is consistent. If we draw a rough graph of both the lines (as shown below) we will find that both lines are parallel.

QUESTION: 2

The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is

Solution:

a_{1} / a_{2} = b_{1} / b_{2} = c_{1} / c_{2}

2/4 = 3/6 = 5/10

1/2 = 1/2 = 1/2

Soa_{1} / a_{2} = b_{1} / b_{2} = c_{1} / c_{2}

When these are equal then it is consistent.

Therefore option (C) is correct .

QUESTION: 3

If am ≠ bl, then the system of equations, ax + by = c, lx + my = n

Solution:

If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.

Given,

Pair of lines represented by the equations

ax + by = c

lx + my = n

For unique solution

For infinite solutions

For no solution

Given,

This can be transformed into

Therefore, If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.

QUESTION: 4

The pair of equations y = 0 and y = - 7 has

Solution:

The equation are y=0 and y=-7

y=0 is on the x-axis and y=-7 is the line parallel to the x-axes at a distance 7 units from y=0

The line will be parallel

if we try to solve these equations we get 0=7 which is absurd.

So the equations are inconsistent.

Therefore there is no solution.

QUESTION: 5

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son. The present ages (in years) of the son and the father are, respectively.

Solution:

Let the present age of father's be x years and present age of son's be y years.

According to the problem

QUESTION: 6

The pair of equations x = a and y = b graphically represents lines which are

Solution:

By graphically in every condition, if a, b>>0; a, b< 0, a>0, b< 0; a<0, b>0 but a = b≠ 0.

The pair of equations x = a and y = b graphically represents lines which are intersecting at (a, b).

If a, b > 0

Similarly, in all cases two lines intersect at (a, b).

QUESTION: 7

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of the number gets reversed. The number is

Solution:

The possibilities are: 18, 27, 36, 45, 54, 63, 72, & 81. A quick addition of 27 to each possibility gives 18+27= 45, 27+27=54, 36+27=63 and 63 is the reverse of 36.

QUESTION: 8

Match the Column:

Solution:

QUESTION: 9

If x = a, y = b is the solution of the pair of equations x - y = 2 and x + y = 4, then the respective values of a and b are

Solution:

QUESTION: 10

A pair of linear equations which has a unique solution x = 2, y = - 3 is

Solution:

### NCERT - Pair of Linear Equations in Two Variables

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