Find whether the pair of linear equations y = 0 and y = -5 has no solution, unique solution or infinitely many solutions.

If ad \(\neq \) bc, then find whether the pairs of linear equations ax + by = p and cx + dy = q has no solution, unique solution or infinitely many solutions.

Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, then find the equation of the second line.

Determine the values of a and b, for which the following pairs of linear equations has infinitely many solutions
3x-(a+1)y=2b-1 and 5x+(1-2a)y=3b

Two straight paths are represented by the lines 7x-5y=3 and 14x-10y=5. Check whether the paths cross each other.

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.

Solve the following pair of equations by substitution method.
1.4x+3.9y=6.4; 0.2x-1.3y=1.2

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

Solve the following pair of equations by elimination method.
\(\frac { x }{ 7 } +\frac { y }{ 3 } =5;\frac { x }{ 7 } -\frac { y }{ 9 } =1\)

Find the values of x and y in the given rectangle.

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

For what value of k, the pair of linear equations kx - 4y = 3, 6x - 12y = 9 has an infinite number of solutions?

Solve the following pairs of linear equations by the substitution method:
\(\sqrt { 2 } x+\sqrt { 3 } y=0\)
\(\sqrt { 3 } x-\sqrt { 8 } y=0\)

Verify that x=2 is a solution of the linear equation 2x+7=13-x.

Use elimination method to find all possible solutions of the following pair of linear equation
2x+3y=8           (1)
4x+6y=7           (2)

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.

Solve graphically the following pair of equations.
2x-y+3=0 and 3x-5y+1=0

Two straight paths are represented by the lines 7x-5y=3 and 21x-15y=5. Check whether the paths cross each other.

The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, then the area is increased by 50 q units. Find the length and the breadth of the rectangle.

For what value of k, the pair of linear equations x+2y=3, 5x+ky+7=0 represents
(i) Intersecting lines
(ii) Parallel lines
Is there any value of k for which the given equations represents coincident lines?

Solve the following pair of linear equation by cross-multiplication method.
2(ax-by)+a+4b=0
2(bx+ay)+b-ra=0

ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadrilateral.