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In the equations \(a_1x+b_1y+c_1=0 \) and \(a_2x+b_2y+c_2=0 \). If \(\dfrac{a_1}{a_2}\ne\dfrac{b_1}{b_2} \), then the equations will represent.
If then the equation will represent intersecting lines
If a pair of linear equations \(a_1x+b_1y+c_1=0 \) and \(a_2x+b_2y+c_2=0 \), represents parallel lines then :
The equation will represent parallel lines of
If a pair of linear equations \(a_1x+b_1y+c_1=0 \) and \(a_2x+b_2y+c_2=0 \) represents coincident lines, then
The equation will represent coincident lines of
The pair of equations \(5x15y=8 \) and \(3x9y=\dfrac{24}{5} \) has
For different values of there will be different value of and vice versa.
Graphically, the pair of equations \(6x3y+10=0 \) and \(2xy+9=0 \) represents two lines which are :
The given equations ARE,
dividing by
…(i)
And …(ii)
Table for
A pair of linear equations which has a unique solution \(x=2,y=3 \) is:
satisfy the equation in (d)
The solution of the pair of equations \(3xy=5 \) and \(x+2y=4 \) is:
…(1)
…(2)
eqn (1)
For what value of \( k\), do the equations \(3xy+8=0 \) and \(6xky=16, \) represent coincident lines?
For what value of \( k\), do the equations \(3xy+8=0 \) and \(6xky=16, \) represent coincident lines?
If the lines given by \(2x+5y+a=0 \) and \(3x+2ky=b \) are coincident, then the value of \(k \) is:
If the lines given by \(2x+5y+a=0 \) and \(3x+2ky=b \) are coincident, then the value of \(k \) is:
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, the years, of the son and the father respectively are :
Let son’s age be years, father’s age =
A/Q
Father’s age years
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, the years, of the son and the father respectively are :
Let son’s age be years, father’s age =
A/Q
Father’s age years
The pair of equations \(x+2y+5=0\) and \(3x6y+1=0\) have
The pair of equations \(x+2y+5=0\) and \(3x6y+1=0\) have
Graphical representation of a system of linear equations \(ax+by+c=0, \ ex+fy=g, \) is not intersecting lines. Also, \(\dfrac{g}{c}\ne\dfrac{f}{b} \). What type of solutions does the system have?
The solution will be no solution
Graphical representation of a system of linear equations \(ax+by+c=0, \ ex+fy=g, \) is not intersecting lines. Also, \(\dfrac{g}{c}\ne\dfrac{f}{b} \). What type of solutions does the system have?
The solution will be no solution
The value of \(c \) for which the pair of equations \(cx y=2\) and \(6x2y=4\) will have infinitely many solutions is :
The value of \(c \) for which the pair of equations \(cx y=2\) and \(6x2y=4\) will have infinitely many solutions is :
The sum of the digits of a twodigit number is 9.If 27 is added to it, digits of the number get reversed. The number is
Let ten’s place be and unit place be
…(1)
…(2)
Solving eqn (1) and (2)
Number is 36
The sum of the digits of a twodigit number is 9.If 27 is added to it, digits of the number get reversed. The number is
Let ten’s place be and unit place be
…(1)
…(2)
Solving eqn (1) and (2)
Number is 36
For what value of \(k \), do the equations \(6x+ky=\ – 16\) and \(3xy+8=0\) represent coincident lines?
For what value of \(k \), do the equations \(6x+ky=\ – 16\) and \(3xy+8=0\) represent coincident lines?
The number of solutions of the pair of linear equations \(x + 2y – 8 = 0 \) and \(2x+4y=16 \) is:
So it has infinitely many solutions
The number of solutions of the pair of linear equations \(x + 2y – 8 = 0 \) and \(2x+4y=16 \) is:
So it has infinitely many solutions
If a pair of linear equations is consistent, then the lines will be :
If a pair of linear equation is consistent, then the lines will be always intersecting
If a pair of linear equations is consistent, then the lines will be :
If a pair of linear equation is consistent, then the lines will be always intersecting
The condition so that the pair of linear equations \(kx+3y+1=0, 2x+y+3=0 \) has exactly one solution is
The condition so that the pair of linear equations \(kx+3y+1=0, 2x+y+3=0 \) has exactly one solution is
If the lines given by \(3x+2ky=2\) and \(2x+5y+1=0\) are parallel, then the value of \( k\) is :
If the lines given by \(3x+2ky=2\) and \(2x+5y+1=0\) are parallel, then the value of \( k\) is :
The pair of linear equations \(kx+2y=5 \) and \( 3x+y=1 \) has unique solution, if :
The pair of linear equations \(kx+2y=5 \) and \( 3x+y=1 \) has unique solution, if :
One equations of a pair of dependent linear equations is –5x + 7y = 2, the second equation can be :
condition for dependent linear equation is
substituting
One equations of a pair of dependent linear equations is –5x + 7y = 2, the second equation can be :
condition for dependent linear equation is
substituting
If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the value of a and b respectively are :
…(1)
…(2)
on solving equation (1) and (2)
If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the value of a and b respectively are :
…(1)
…(2)
on solving equation (1) and (2)
The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0 has :
The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0 has :
The pair of linear equations 2x + 5y = 3 and 6x + 15y = 12 represent :
The pair of linear equations 2x + 5y = 3 and 6x + 15y = 12 represent :