Solve the following pair of linear equations.
41x+53y=135 and 53x+41y=147

3

(a)

If the lines given by 2x+Ky=1 and 3x-5y=7 has unique solution, then find the value of K.

3

(a)

Find the value of 'k' for which the system of equations kx-5y=2; 6x+2y=7 has no solution.

3

(a)

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

3

(a)

The sum of a two-digit number and number obtained by reversing the order of digits 99. If the digits of the number differ by 3, then find the numbers.

3

(a)

Find the point of intersection of lines 2ax-by=2a²-b² and ax+2by=a²+2b² by eliminating the variables. Show that the system of equations is concurrent with the line represented by equation (a-b)x+(a+b)y=a²+b².

3

(a)

Solve the following pair of linear equations.
\(\frac { x }{ 7 } +\frac { y }{ 3 } =a+b;\frac { x }{ { a }^{ 2 } } +\frac { y }{ { b }^{ 2 } } =2,\quad a,b\neq 0\)

3

(a)

Solve the following pair of linear equations.
ax+by=1; bx+ay=\(\frac { 2ab }{ { a }^{ 2 }+{ b }^{ 2 } } \)

3

(a)

Represent the following pair of linear equations graphically. Find the points, where the lines intersect the Y-axis.
3x+y-5=0; 2x-y-5=0

3

(a)

Form a pair of linear equations in two variables using the following information and solve it graphically. Five years ago, Sagar was twice as old as Tim. Ten years later; Sagar's age will be ten years more than Tiru's age. Find their present ages.

3

(a)

Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x - y = 1. How many such lines can we find?

3

(a)

Determine algebraically, the vertices of the triangle formed by the lines
3x-y=3, 2x-3y=2 and x+2y=8.

3

(a)

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically.x + y = 5, 2x + 2y = 10

3

(a)

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically x - y = 8, 3x - 3y = 16

3

(a)

Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines.

3

(a)