Find a, if the line 3x+ay=8 passes through the intersection of lines represented by equations 3x-2y=10 and 5x+y=8.

2

(a)

There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.

2

(a)

If the angles of a triangle are x, y and 40⁰ and the difference between the two angles x and y is 30⁰ . Then, find the values of x and y.

2

(a)

Solve the following pair of equations by elimination method.
2x+3y-5=0; 3x-2y-14=0

2

(a)

Solve the following pair of equations by elimination method.
3x+2y=7; 2x-5y+8=0

2

(a)

Solve the following pair of equations by elimination method.
11x+15y+23=0; 7x-2y-20=0

2

(a)

The sum of two numbers is 120 and one of the numbers is 3 times the other. Find the value of the numbers.

2

(a)

The combined ages of two people is 34. If one person is 6 yr younger than the other, then find their ages.

2

(a)

Equation 2x=5y+4 is given. Write another linear equation, so that the lines represented by the pair are
(i) intersecting
(ii) coincident
(iii) parallel

2

(a)

On comparing the ratios \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } ,\frac { { b }_{ 1 } }{ { b }_{ 2 } } and\frac { { c }_{ 1 } }{ { c }_{ 2 } } \), whether the following pairs of linear equations are consistent or inconsistent: 
2x- 3y = 7

2

(a)

On comparing the ratios \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } ,\frac { { b }_{ 1 } }{ { b }_{ 2 } } and\frac { { c }_{ 1 } }{ { c }_{ 2 } } \), whether the following pairs of linear equations are consistent or inconsistent:
5x-3y = 11,-10x + 6y = -22

2

(a)

Given the linear equation 3x + 4y = 9. Write another linear equation in these two variables such that the geometrical representation of the pair so formed is :
(i) intersecting lines
(ii) coincident lines

2

(a)

For what value of k, 2x + 3y = 4 and (k + 2)x + 6y = 3k + 2 will have infinitely many solutions?

2

(a)

For what the value of 'k', the system of equations kx + 3y = 1, 12x + ky = 2 has no solution.

2

(a)

Solve 2x + 3y = 11 and 2x - 4y = - 24 and hence find the value of m for which y = mx + 3.

2

(a)