Inconsistent Pair of Linear Equations

Q.

The pair of equations y = 0 and y = -7 has :

1. One Solution

2. Infinitely Many Solutions

3. No Solution

4. Two Solutions

Q.

For what value of k, the pair of equations 4x-3y=9, 2x+ky=11 has no solution

Q.

What is the formula of unique solution?

Q.

$A_{1}x+B_{1}y+C_1=0$, $A_{2}x+B_{2}y+C_2=0$is a system of two simultaneous linear equations, if $\left(\frac{A_1}{A_2}\right)=\left(\frac{B_1}{B_2}\right)=\left(\frac{C_1}{C_2}\right)$ then the system has ________ solution.

Q.

If a pair of linear equations is inconsistent then their graph lines will be

(a) parallel (b) always coincident

(c) always intersecting (d) intersecting or coincident

Q.

Given the linear equation $2x+3y-8=0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is

(ii) Parallel lines

Q. Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :

3x − 5y = 20
6x − 10y = −40

Q.

Question 3 (ii)
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 pair of linear equations are consistent, or inconsistent.
2x - 3y = 8 ; 4x - 6y = 9

Q.

Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:

Q. lines do not intersect each other.

1. Non parallel
2. Parallel
3. coincident

Q. Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :

2y − x = 9
6y − 3x = 21

Q.

Find the equations of the line passing through the points:

(ii) $(0,-3)$ and $(5,0)$

Q. Question 4 (ii)
Find the value(s) of p for the following pair of equations – x + py = 1 and px – y = 1, if the pair of equations has no solution.

Q. Which of the following pairs of equations is inconsistent?

1. $2x+3y=15;4x+7y=11$
2. $4x+y=12;8x+2y=24$
3. $x+2y=5;2x+4y=15$
4. $11y+3x=1;5y+2x=7$

Q.

How do you solve an augmented matrix $?$

Q.

The equation $x+2y+2z=1$ and $2x+4y+4z=9$ have

1. Only one solution

2. Only two solutions

3. Infinite number of solutions

4. None of these

Q.

Is the pair of equations $3x–5y=6$ and $4x–6y=7$ consistent$?$ Justify your answer.

Q. Question 4 (ii)
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Q. Do the equations 5x+7y=8 and 10x+14y=4 represent a pair of concident lines ? Justify your answer.

Q.

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.

Q. For which value of k will the following pair of linear equations have no solution?
$3x+y=1$
$(2k-1)x+(k-1)y=2k+1$

1. $k=4$
2. $k=1$
3. $k=2$
4. $k=5$

Q.

The system of pair of equations $4x-3y+12=0$ and $2x+3y-15=0$ has

1. infinitely many solutions

2. no solution

3. 2 solutions

4. a unique solution

Q. Show graphically that each one of the following systems of equations has infinitely many solutions:

2x + 3y = 6
4x + 6y = 12

Q.

Which of the following pairs of linear equations is inconsistent?
$1.x+3y–5=0,2x+y=0$
$2.2x+y=1,2y=2–4x$
$3.2x–y=2,2y–4x=2$

1. All of the above.

2. $x+3y–5=0,2x+y=0$

3. $2x–y=2,2y–4x=2$

4. $2x+y=1,2y=2–4x$

Q. The graphs of the equations $2x+3y-2=0\mathrm{and}\mathrm{x}-2\mathrm{y}-8=0$ are two which are

(a) coincident
(b) parallel
(c) intersecting exactly at one point
(d) perpendicular to each other

Q.

Which of the following equations have a unique solution or infinitely many solutions.

(i) $x-3y-3=0;3x-9y-2=0$

(ii) $2x+y=5;3x+2y=8$

1. option (ii) is correct.

2. option (i) is correct.

Q. If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is ...................

1. inconsistent.
2. None of above
3. consistent.
4. Cannot be determined

Q.

We can multiply ___ of the equation by the same non-zero number.

Q. The graphs of the equations $5x-15y=8\mathrm{and}3x-9y=\frac{24}{5}$ are two which are
(a) coincident
(b) parallel
(c) intersecting exactly at one point
(d) perpendicular to each other

Q. The pair of linear equations $6x-3y+10=0,2x-y+9=0$ has
(a) one solution
(b) two solutions
(c) many solutions
(d) no solution