If a pair of linear equations is consistent then the lines will ______
- Intersect
- be coincident
- be parallel
- intersect or coincident
The pair of equations x = 2 and y = - 2 has _______
- One solution
- Two solution
- Infinitely many solutions
- No solutions
Graphically, the pair of equations 3x + 2y = 16, 5x + y = 18 represents two lines which are _______
- intersecting at exactly one point
- parallel
- Intersecting at exactly two points
- Coincident
If the lines given by ax−y=3 and 21x−3y=9 will have infinitely many solutions, then the value of a is ______
- 4
- 3
- 7
- 9
The equations given by the lines x = h and y = k represent_______
- coincident lines
- parallel lines
- intersecting lines at point (h, k)
- intersecting lines at (0, 0)
If am = bl and bn≠cm,then the system of equations ax+by=c & lx+my=n
- Has a unique solution.
- Has no solution.
- Has infinitely many solutions.
- May or may not have a solution.
Indetify which one among the following is the pair of linear equations having a unique solution x = - 3, y = 2
- 2/3x+7/2y=10 and 5x+3y=9
- √3x−3y=3√3andx+7y=11
- 3y=13x+45and−7x+3y=27
- none
If (C, C) is the solution of system of equations mx+n y+(s−t)=0 and nx+my(r−s)=0, (m≠n), then
- 2s = r + t
- 2r = s + t
- 2t = s + t
- r = s + t
How many values of c, for which the system of equations 6x+3y=c−3, 12x+cy=c has infinitely many solutions?
- 1
- 2
- 3
- None
If the system of equations 2x+3y=7 & 2ax+(a+b)y=28 has infinitely many solutions, then the values of a and b respectively are ____.
- 2, 5
- 5 ,8
- 4 ,8
- 3 ,6
The value of k, for which the system of equations kx−3y+6=0, 4x−6y+15=0represent parallel lines, is ____.
- 1
- 2
- 3
- 4
- x=3, y=12
- x=4, y=36
- x=16, y=25
- x=9, y=49
Find the values of p and q for which the pair of linear equations have infinitely many solutions.
(3 p + 2q) x + (q + 2p) y = 3p - q + 14x + 7y = 29
- −5/7,2/7
- 2/7,13/14
- −5/7,13/14
- None
Value of x in pair of linear equations 36x+24y=702and 24x+36y=558is
- 33/2
- 145/7
- 16
- 17
Which of the following linear equation coincide with the line4x+5y=15?
- 8x+10y=25
- 2x+3y=7
- 7x+14y=17
- 12x+15y=45
What is the condition that a system of simultaneous equations a1x+b1y+c1=0 and a2x+b2y+c2=0must satisfy to have exactly one solution?
- a1/a2=b1/b2
- a1/a2≠b1/b2
- a1/a2=c1/c2
- b1/b2=c1/c2
How many solutions do the equations satisfying (a₁⁄a₂)=(b₁⁄b₂)=(c₁/c₂) have?
- 1
- 2
- 3
- infinite
What is a system of simultaneous equations called if it has no solution?
- Consistent system
- independent system
- inconsistent system
- Dependent system
How many solutions does the system of equations p+2q=4and2p+4q−12=0 have?
- 0
- 1
- 2
- 3
What is a system of simultaneous equations called if its graph has intersecting lines?
- Inconsistent system
- consistent system
- Dependent system
- independent system
What is the nature of the graphs of a dependent system?
- Parallel lines
- Perpendicular lines
- Intersecting lines
- Coincident lines
What is the nature of the graphs of a system of linear equations with exactly one solution?
- Parallel lines
- Perpendicular lines
- Coincident lines
- Intersecting lines
Which of the following is a consistent system of simultaneous equations?
- m+3n=6
2m+6n=12 - a + 3b = 6
2a−3b=12 - x−4y=6
2x−8y=12 - l−2m=63
l−6m=12
What is the number of solutions of the pair of linear equations4p−6q+18=0and2p−3q+9=0?
- 0
- 1
- 2
- infinite
Find the unique solution of the system of simultaneous equations2x−y=2 and4x−y=4.
- x=0,y=1
- x=0,y=0
- x=1,y=0
- x=1,y=1
Choose the dependent system from the following.
- m+n=7
3m+3n=21 - 3x−2y=52x−3y=7
- 3x−3y=18x−y=10
- 2x+y=64x−2y=4
The system of simultaneous equations 3m+n=1and(2k−1)m+(k−1)n=2k+1, is inconsistent. What is the value of 'k'?
- 3
- 2
- 1
- 0
If the pair of linear equations3x+5y=3 and 6x+ky=6 do not have any solution, which of the following is true?
- k = 5
- k = 10
- k≠10
- k≠5
If the pair of equations 3x+5y=k and9x+12y=6has infinitely many solutions, which of the following is true?
- k=2
- k=6
- k≠6
- k=3
What type of a system of equations is the pair of linear equations 2x - 3y = 8 and 4x - 6y = 9?
- Consistent system
- inconsistent system
- Dependent system
- independent system
