Conditions to Find the Solution of Equations

Q. Consider two equations in the variables x and y written in the standard form:
$a_{1}x+b_{1}y+c_1=0and$
$a_{2}x+b_{2}y+c_2=0$
have the coefficients as follows:
$a_1=5,b_1=6,c_1=4,a_2=10,b_2=12,c_2=7$.
What is the nature of these two lines?

1. Coincident
2. Intersecting
3. Parallel
4. Coincident or parallel

Q. Question 6 (i)
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:
(i) Intersecting lines

Q.

If $px+qy+r=0$ represent a family of straight lines such that $3p+2q+4r=0$ then

1. All lines are parallel

2. All lines are inconsistent

3. All lines are concurrent at $\left(\frac{3}{4},\frac{1}{2}\right)$

4. All lines are concurrent at $(3,2)$

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-ii, B-i, C-iii

2. A-ii, B-iii, C-i

3. A-iii, B-i, C-ii

4. A-i, B-iii, C-ii

Q. Two equations in the variables $x$ and $y$ written in the standard form, where
$a_{1}x+b_{1}y+c_1=0and$
$a_{2}x+b_{2}y+c_2=0$,
have the coefficients as follows:
$a_1=5,b_1=6,c_1=4,a_2=10,b_2=12,c_2=7$
What is the nature of these two lines?

1. Coincident
2. Intersecting
3. Parallel
4. Coincident or parallel

Q. The graphical representation of the pair of equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 is?

1. Intersecting lines
2. Parallel lines
3. All of these
4. Coincident lines

Q.

Match the following:
$\begin{array}{cc}\text{A}.y=-\frac{3}{2}-\frac{x}{2};x=-3-2y& \text{(i)Inconsistent pair}\\ \text{B}.5x=6-3y;9y=12-15x& \text{(ii)Dependent pair}\\ \text{C}.y=\frac{2}{7}-\frac{x}{7};y=\frac{18}{5}-\frac{x}{5}& \text{(iii)Unique solution}\end{array}$

1. A-iii, B-i, C-ii

2. A-i, B-iii, C-ii

3. A-ii, B-i, C-iii

4. A-ii, B-iii, C-i

Q.

Two equations in the variables $x$ and $y$ written in the standard form where
$a_{1}x+b_{1}y+c_1=0and$
$a_{2}x+b_{2}y+c_2=0$,
have the coefficients as follows:
$a_1=5,b_1=6,c_1=4,a_2=10,b_2=12,c_2=7$.
What is the nature of these two lines?

1. Coincident

2. Intersecting

3. Coincident or parallel

4. Parallel

Q.

Two equations in the variables $x$ and $y$ written in the standard form where
$a_{1}x+b_{1}y+c_1=0and$
$a_{2}x+b_{2}y+c_2=0$,
have the coefficients as follows:
$a_1=5,b_1=6,c_1=4,a_2=10,b_2=12,c_2=7$.
What is the nature of these two lines?

1. Coincident

2. Parallel

3. Coincident or parallel

4. Intersecting

Q.

Match the following:
$\begin{array}{cc}\text{A}.y=-\frac{3}{2}-\frac{x}{2};x=-3-2y& \text{(i)Inconsistent pair}\\ \text{B}.5x=6-3y;9y=12-15x& \text{(ii)Dependent pair}\\ \text{C}.y=\frac{2}{7}-\frac{x}{7};y=\frac{18}{5}-\frac{x}{5}& \text{(iii)Unique solution}\end{array}$

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