Which of the following pair of linear equations is inconsistent?
Pair of linear equations are inconsistent when they are parallel. When the two equations are parallel ,we have .
In D, we have which is , so it is inconsistent.
The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:
We have a1, a2 the coefficients of x2,b1 and b2 coefficients of x and c1 and c2 the constant terms.So,a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.
The pair of linear equations 8x – 5y = 7 and 5x – 8y = -7 have :
So, they are intersecting lines. And intersecting lines meet at only one point. So only 1 solution is available.
One equation of a pair of dependent linear equations is -5x + 7y = 2, the second equation can be :
If a system of two linear equation is consistent system and has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.So we have which is satisfied by 10x – 14y = -4 only.
Which of following is not a solution of 3a + b = 12?
The number of solutions of the pair of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 are:
We have the equations x + 2y – 8 = 0 and 2x + 4y = 16 Where
Here which is the case of coincident lines . So there are infinitely many solutions.
The pair of linear equations 3x + 2y = 5 and 2x – 3y = 7 will have
If the pair of equation has no solution, then the pair of equation is :
The pair of equations has no solutions ,this means that the two equation does not have a common point which means that they does not meet each other anywhere.So the pair of lines which does not meet anywhere are parallel lines and parallel lines are inconsistent.
Which of the following equation is not a linear equation?
Linear equation is an equation between two variables that gives a straight line when plotted on a graph. Linear equations have degree 1 only which means that power of the variables is 1 only. Since does not have degree 1 its not a linear equation.
A system of simultaneous linear equations has infinitely many solutions if two lines:
The pair of equations y = 0 and y = -7 has :
y=0 is x-axis… since every point has y=0. y=-7 is a line parallel to x-axis passing through x=0,y=-7. So the two lines are parallel to each other and are inconsistent which means that it has no solutions because it will never meet.
The following pair of linear equations 3x – 2y + 5 = 0, 5x + 7y = 2 will have
For what value of ‘K’ will the system of equations: 3x + y = 1, (2K – 1) x + (K – 1) y = 2K + 1 have no solution
is a case of parallel lines which never meet. So there are no solutions obtainable for these equations. So equations are inconsistent
3x + y = 1, (2K – 1) x + (K – 1) y = 2K + 1
Which of the following pairs of equations represent inconsistent system?
is a case of parallel lines which never meet. So there are no solutions obtainable for these equations. So equations are inconsistent.
3x – y = -8 ,3x – y = 24
3x – y +8=0 ,3x – y -24=0
So, Therefore the equations are inconsistent.
Which of the following is not a solution of pair of equations 3x – 2y = 4 and 6x – 4y = 8?
3x – 2y = 4 and 6x – 4y = 8
Putting x=5 and y=3
LHS ≠ RHS
6(5)-4(3)=30-12=18 ≠ 8