Linear Equations in Two Variables

Q. The intersecting point of the graphs of the given two linear equations is

1. (2, 3)
2. (4, 3)
3. (3, 2)
4. (3, 4)

Q. ax + by + c = 0; if b = 0, then the line will always be parallel to the .

1. x-axis
2. y-axis
3. z-axis

Q. Graphically represent the following pair of linear equation in two variable:
y-2x-4=0 and
2y=6x+12
also find there solution.

Q.

Which of the following are Pair of Linear Equation in two variables?

1. x + 2 = 0; a + 2b = 0

2. x + y - 3 = 0; 4a + 2b + c = 24

3. 2x + y = 2; 3x - z=2

4. 12x + 4y + 3 = 0; 4x + 4y + 4 = 0

Q.

Use graph paper for this question.

Plot the points A(-2, 0), B(4, 0), C(1, 4) & D(-2, 4).

Draw the line of symmetry of ∆ABC, name it L₁.

Point D is reflected about L₁ to get image E.

a) Write coordinates of E

b) Write equations of the lines of symmetry of figure ABED

1. E(2 , 4)

   = 2, y = 1

2. E(4 , 4)

   = 1, y = 1

3. E(2 , -4)

   = -2, y = 2

4. E(2 , 4)

   = 0, y = 2

5. E(4 , 4)

   = 1, y = 2

6. E(-2 , 4)

   = -1, y = 2

7. E(4 , 4)

   = 0, y = 2

Q. If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.

Q.

Draw the graph of the following linear equations in two variables: $y=3x$

Q. What are the values of $c_1$ and $c_2$, when the following equations are represented in their standard form: $ax+by+c=0$
$\left(i\right)4y=7x-3$
$\left(ii\right)11x+2y=-2$

1. $c_2=7or-7$ and $c_1=11or-11$.
2. $c_1=4or-4$ and $c_2=2or-2$.
3. None of the above.
4. $c_1=3or-3$ and $c_2=2or-2$.

Q. If the system of equations is inconsistent, then k =

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

(a) 1
(b) 0
(c) −1
(d) 2

Q. If $3x–4y=1$ and $5x–6y=7,$ then $x+y$ = ___.

1. 16
2. 20
3. 18
4. 19

Q.

Solve the following pair of linear equations.
(a−b)x+(a+b)y=a²−2ab−b²

(a+b)(x+y)=a²+b²

Q. If the pair of linear equations $x+2y-4=0$ and $2x+4y-12=0$ are plotted graphically, we get solution(s).

1. Infinite
2. Unique
3. zero

Q. Which of the following can’t be represented in standard form $ax+by+c=0$ of a linear equation?

1. $2x+y+\frac{x}{y}=0$
2. $y=6$
3. $2x+5y=0$
4. $5x+6=0$

Q.

1. x+2y=0

2. x+y=0

3. 2x-y=0

4. x-2y=0

Q.

Which of the following equations is written in standard form?

1. 2x + 3y - 6 = 0

2. 2x = 3y - 7

3. y = 2x + 3

4. y + 7 = x

Q. Write a pair of linear equations which has the unique solution x=1 and y=-3.

Q. 18.Find the value of P , such that the linear equation 6x-Py=0 has equal values x and y . Where x is not equal to zero

Q. How many solutions can the equation 5x + 4y = 2 have?

1. Infinite
2. One
3. Two
4. Data inadequate

Q.

Question 6
Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

Q.

Find the solution to the following system of linear equations:

0.2x + 0.3y = 1.2
0.1x - 0.1y = 0.1

1. (2, 1)

2. (1, 2)

3. (2, 3)

4. (3, 2)

Q.

For what value of k, the pair of linear equations 3x + ky = 9 and 6x + 4y = 18 will have infinitely many solutions?

1. 2

2. 1

3. -5

4. 6

Q. For which value's of $a$ & $b$ does the following pair of linear equation have an infinite number of solution
$2x+3y=7$
$(a-b)x+(a+b)y=3a+b-2$

Q. Given two equations :
$3x–4y=1$ ---------- (1)
$5x–6y=7$ ---------- (2)
What has to be done so that the coefficients of $x$ are equal?

1. Multiply equation (1) by 6 and equation (2) by 4.
2. Multiply equation (1) by 3 and equation (2) by 5.
3. Multiply equation (1) by 5 and equation (2) by 3.
4. None of the above

Q. Which of the following can be considered as an algebraic equation?

1. $3x^2+7y+3=0$
   
2. $3x+4y\le 8$
3. 5 + 67 = 80 - 8
4. 2x + 77 > 3

Q.

Which of the following are a pair of linear equations in two variables?

1. 2x + y = 2; 3x - z=2

2. x + 2 = 0; a + 2b = 0

3. 12x + 4y + 3 = 0; 4x + 4y + 4 = 0

4. x + y - 3 = 0; 4a + 2b + c = 24

Q. We have two equations
$3x–4y=1$ ---------- (1)
$5x–6y=7$ ---------- (2)
In the above equations, to equate the coefficients of x, what has to be done?

1. Multiply equation (1) by 5 and equation (2) by 3
2. Multiply equation (1) by 7 and equation (2) by 1
3. Multiply equation (1) by 6 and equation (2) by 4
4. Multiply equation (1) by 3 and equation (2) by 5

Q. Compare x + 3y - 3 = 0 with the standard form and choose the correct alternative.

1. a = 1, c = 3
2. a = 1, c = 4
3. a = 1, b = 3
4. a = 3, c = 3

Q.

Represent 0.131313….. In a rational form. [2MARKS]

Q.

The graph of the equation $2x-3=3x-5$ is parallel to:

1. $x$-axis

2. $y$-axis

3. Both the axes

4. None of the axes

Q.

Draw the graphs of the following equations on the same graph paper:

2x + 3y = 12

x - y = 1.

Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis.