Linear Equations In Two Variables MATHS - Linear Equations In Two Variables

If (2k - 1, k) is a solution of the equation 10x - 9y = 12, then k =

1. 1
2. 2
3. 3
4. 4

The distance between the graph of the equations x = -3 and x = 2 is:

1. 1
2. 2
3. 3
4. 5

lf the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB is of length:

1. 4 units.
2. 3 units.
3. 5 units.
4. None of these.

x = 2, y = -1 is a solution of the linear equation:

1. x + 2y = 0
2. x + 2y = 4
3. 2x + y = 0
4. 2x + y = 5

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is:

1. 3
2. 1
3. 2
4. 4

From the choices given below, choose the equation whose graph is given in Fig.

1. y = x + 2
2. y = x - 2
3. y = -x + 2
4. x = 2y = 6

[Hint: Clearly (2, 0) and (-1, 3) satisfy the equation y = -x + 2]

Write the following as an equation in two variables:
y = 3

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
4 = 3x

From the choices given below, choose the equation whose graph is given in Fig.

1. y = x
2. x + y = 0
3. y = 2x
4. 2 + 3y = 7x

[Hint: Clearly, (-1, 1) and (1, -1) satisfy the equation x + y = 0]

Write the equation of a line parallel to y-axis and passing through the point (-3, -7).

Write the equation of a line passing through the point (3, 5) and parallel to x-axis.

The sum of a two digit number and the number obtained by reversing the order of its digits is 121. lf units and ten's digit of the number are x ard y respectively, then write the linear equation representing the above statement.

A number is 27 more than the number obtained by reversing its digits. If its unit's and ten's digit are x and y respectively, write the linear equation representing the above statement.

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
5x - 2y = 10

Give the geometric representations of the following equations:

1. On the number line.
2. On the Cartesain plane.

x = 2

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
2x + 3y = 24

Give the geometric representations of the following equations:

1. On the number line.
2. On the Cartesain plane.

y = 3

Draw the graph of the equation 2x + y = 6. Shade the region bounded by the graph and the coordinate axes. Also, find the area of the shaded region.

Draw the graph of the equation 2x + 3y = 12. From the graph, find the coordinates of the point:

1. Whose y-coordinates is 3.
2. whose x-coordinates is -3.

Ravish tells his doughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be".. lf present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.

Draw the graph of y = |x|.

Draw the graph of the following linear equations in two variables:
x + y = 4

Draw the graph of the following linear equations in two variables:
y = 2x

Draw the graph of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes:
6x - 3y = 12

Draw the graph of the following linear equations in two variables:
2y = -x + 1