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

If am=bl, then find whether the pair of linear equations ax + by = c and lx + my = n has no solutions, 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.

Father's age is 3 times the sum of ages of his two children. After 5 yr, his age will be twice the sum of ages of the two children. Find the age of father.

For what value of k, the pair of equations kx+2y=5, 3x-4y=10 has no solution?

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

Solve the pair of linear equations by cross-multiplication method.
4x+y=-1; 7x+y=-4

On comparing the ratios \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } ,\frac { { b }_{ 1 } }{ { b }_{ 2 } } and\frac { { c }_{ 1 } }{ { c }_{ 2 } } \), find out whether the following pairs of linear equations are consistent or inconsistent:
3x + 2y = 5; 2x - 3y = 7

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

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

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.

A fraction becomes \(\frac {4}{5}\)  if 2 is added to both numerator and denominator, if however 4 is subtracted from both numerator and denominator, then the fraction becomes \(\frac {1}{2}.\)Represent this situation2 algebraically and graphically.

Solve the following system of equations by cross-multiplication.
x+y=a+b and ax-by=a² -b²

Form the pair of linear equations for the following problems and find their solution by substitution method.
A fraction becomes \(\frac { 9 }{ 11 } \), if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes \(\frac { 5 }{ 6 } \). Find the fraction.

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross-multiplication method.x-3y -7 = 0 ,3x - 3y - 15 = 0

Solve graphically, the pair of linear equations x-y=-1 and 2x+y-10=0. Also, find the vertices of the triangle formed by these lines and X-axis.

Find the value of k, for which system of equations kx+3y=3 and 12x+ky=6 represent parallel lines.

Students were standing in rows for a mass drill. if one student is extra in a row, there would be 2 rows less. If one students is less in a row, there would be 3 rows more. Find the number of students.

On comparing the ratios \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } ,\frac { { b }_{ 1 } }{ { b }_{ 2 } } \) and \(\frac { { c }_{ 1 } }{ { c }_{ 2 } } ,\) find out whether the lines representing the following pair of linear equations intersect at a point are parallel or coincident.
 5x-4y+8=0; 7x+6y-9=0