Dependent Pair of Linear Equations

Q.

Question 9
One equation of a pair of dependent linear equations is - 5x + 7y – 2 = 0
(A) 10x + 14y + 4 = 0
(B) –10x – 14y + 4 = 0
(C) –10x + 14y + 4 = 0
(D) 10x – 14y = –4

Q. Dependent pair of linear equations is always ___.

1. continuous
2. consistent
3. inconsistent
4. recurring

Q.

Write any one solution of equation $x+2y=7$.

Q.

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions:

$kx+3y=(2k+1)2(k+1)x+9y=(7k+1).$

Q. Dependent pair of linear equations is always.

1. consistent
2. inconsistent
3. non-intersecting

Q.

For what value of $\mathrm{k}$ the following system of linear equations will have no solution?

$$\begin{gathered} 3\mathrm{x}+\mathrm{y}=1 \\ (2\mathrm{k}-1)\mathrm{x}+(\mathrm{k}-1)\mathrm{y}=2\mathrm{k}+1 \end{gathered}$$

Q.

Obtain the condition for the following system of linear equations to have a unique solution

ax + by = c

lx + my = n

Q. The value of k for which the following system of linear equations represent coincident lines is
2x + 9y = k; 6x + 27y = 5

1. $\frac{3}{5}$
2. $\frac{2}{3}$
3. $\frac{5}{3}$
4. $\frac{6}{5}$

Q. One equation of a pair of dependent linear equations is $-5x+7y=2,$ the second
equation can be :

1. $10x-14y=-4$
2. $-10x+14y+4=0$
3. $-10x-14y+4=0$
4. $10x+14y+4=0$

Q. If pb = aq, qc = br and pc = ar, then the system of equations px + qy = r and ax + by = c (a, b, c, p, q, r ≠ 0)

1. Has a unique solution
2. Has no solution
3. Has infinitely many solutions
4. Has exactly two solutions

Q.

Find the values of a and b for which each of the following systems of linear equations has an infinite number of equations:

$2x+3y=7,(a+b+1)x+(a+2b+2)y=4(a+b)+1.$

Q. The pair of linear equations $y=-\frac{3}{2}-\frac{x}{2};x=-3-2y$ are a pair of dependent equations

1. True
2. False

Q. Match the following with their type of lines.

1. Parallel
2. Intersecting
3. Coincident

Q.

Which of the following represents a pair of dependent equations?

1. $y=-\frac{3}{2}-\frac{x}{2};x=-3-2y$

2. $5x=6-3y;9y=12-15x$

3. $y=\frac{2}{7}-\frac{x}{7}$; $x=\frac{2}{7}-\frac{y}{7}$

4. $3x=6-3y;10y=12-15x$

Q. Solve the following system of linear equations in three variables
$$3x-2y+z=2,2x+3y-z=5,x+y+z=6\text{.}$$

Q. Match the following with their type of lines.

1. Parallel
2. Intersecting
3. Coincident

Q. Which among the following pairs of linear equations have no solution?

1. 
2. 

Q.

For which value(s) of λ, do the pair of linear equations λx + y = \lambda ^{2} and x + λy = 1 have

(i) no solution?

(ii) infinitely many solutions?

(iii) a unique solution?

Q.

Find the value of k for which each of the following systems of equations have infinitely many solution: (9-19)

2x + 3y - 5 =0

6x + ky - 15 = 0

Q. Match the following:
$\begin{array}{cccc}A.& y=-\frac{3}{2}-\frac{x}{2};x=-3-2y& \left(i\right)& Inconsistentpair\\ B.& 5x=6-3y;9y=12-15x& \left(ii\right)& Dependentpair\\ C.& y=\frac{2}{7}-\frac{x}{7};y=\frac{18}{5}-\frac{x}{5}& \left(iii\right)& Uniquesolution\end{array}$

1. A-ii, B-iii, C-i
2. A-iii, B-i, C-ii
3. A-i, B-iii, C-ii
4. A-ii, B-i, C-iii

Q.

Total number of solutions to the system of linear equations $x+y+z=1,2x+2y+2z=3,$
$x+y=1$ is infinity.

1. True

2. False

Q. Match the following:
$\begin{array}{cc}A.y=-\frac{3}{2}-\frac{x}{2};x=-3-2y& \left(i\right)Inconsistentpair\\ B.5x=6-3y;9y=12-15x& \left(ii\right)Dependentpair\\ C.y=\frac{2}{7}-\frac{x}{7};y=\frac{18}{5}-\frac{x}{5}& \left(iii\right)Uniquesolution\end{array}$

1. A-i, B-iii, C-ii
2. A-ii, B-i, C-iii
3. A-ii, B-iii, C-i
4. A-iii, B-i, C-ii

Q. If $3x+y=11$ and $(m+n)x+(m–n)y=5m+n$ has infinitely many solutions, then the value of m and n respectively can be

1. 6, 4
2. 5, 1
3. 6, 3
4. 3, 6

Q. Find the values of $\alpha +\beta$ for which the following system of linear equations has infinite number of solutions $2x+3y=7$ & $2\alpha x+(\alpha +\beta )y=28$

Q. Question 3
For what values of a and b will the following pair of linear equations have infinitely many solutions?
x + 2y = 1
(a - b)x + (a + b)y = a + b - 2

Q. Find the value of $k$ for which the equations $kx+2y=5$, $3x+y=1$ has a unique solution.

1. 6

Q.

Question 1 (ii)
For which value(s) of $\lambda$ does the pair of linear equations $\lambda x+y={\lambda }^{2}andx+\lambda y=1$ have infinitely many solutions?

Q. The set of equations 2x+3y+4z=0, 3x+4y+6z=0, 4x+5y+8z=0

1. Infinite solutions
2. is inconsistent
3. has unique solution
4. has two solutions

Q. Match the following with their type of lines.

1. Parallel
2. Intersecting
3. Coincident

Q.

Which of the following represents a pair of dependent equations?

1. $5x=6-3y;9y=12-15x$

2. $y=-\frac{3}{2}-\frac{x}{2};x=-3-2y$

3. $y=\frac{2}{7}-\frac{x}{7}$; $x=\frac{2}{7}-\frac{y}{7}$

4. $3x=6-3y;10y=12-15x$