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Pair of Linear Equations in Two Variables

Multiple Choice Questions

31. The graph of x + y = 10 and y - x = 4 will intersect at a point:

(-3,7)
(3,7)
(2,7)
(2,7)

205 Views

32. The graph of y = kx; K = constant will always :

Intersect y-axis
x-axis
Passes through the origin
Passes through the origin

126 Views

33. The solution of 8x + 5y = 9 and 3x + 2y = 4 is

(-2,5)
(2,5)
(3,5)
(3,5)

120 Views

34. The equations x + y = 3; 3x - 2y = 4 inlerseet at:

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

111 Views

35. For what value of ‘a’ the pair of equations: 3x + 2y - 4 = 0; ax - y - 3 = 0 liasa unique solution.

$space space space straight a not equal to 3 over 2 space space space space space space space space$
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$space straight a not equal to 3 space space space space space space space$
$space straight a not equal to 3 space space space space space space space$

100 Views

Short Answer Type

36. Solve the following pairs of linear equations by the substitution method.

x + y = 14
x – y = 4

139 Views

37.

Solve the following pair of linear equations by the substitution method

s - t = 3

"<pre

99 Views

38.

Solve the following pairs of linear equations by the substitution method.
3x – y = 3
9x – 3y = 9

172 Views

39.

Solve the following pairs of linear equations by the substitution method.
0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3

214 Views

40.
Solve the following pairs of linear equations by the substitution method.
$square root of 2 straight x end root plus square root of 3 straight y end root equals 0 square root of 3 straight x end root minus square root of 8 straight y end root equals 0$

square root of 2 straight x end root plus square root of 3 straight y end root equals 0 square root of 3 straight x end root minus square root of 8 straight y end root equals 0

The given pair oflinear eqn. is

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From eq. (ii), we have

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Substituting this value of a in equation (i), we get

square root of 2. fraction numerator square root of 8 over denominator square root of 3 end fraction straight y plus square root of 3 straight y equals 0 rightwards double arrow space fraction numerator 4 over denominator square root of 3 end fraction straight y plus square root of 3 straight y end root equals 0 rightwards double arrow space open parentheses fraction numerator 4 over denominator square root of 3 end fraction plus square root of 3 close parentheses straight y equals 0 rightwards double arrow space space space space space space straight y equals 0

Substituting this value of y in eqn. (iii), we get

straight x equals fraction numerator square root of 8 over denominator square root of 3 end fraction left parenthesis 0 right parenthesis equals 0

Therefore, the solution is

x = 0, y = 0

Verification. Substituting x = 0 and y = 0, we find that both the equation (i) and (ii) are satisfied as shown below :

$square root of 2 straight x end root plus square root of 3 straight y end root equals square root of 2 left parenthesis 0 right parenthesis plus square root of 3 left parenthesis 0 right parenthesis equals 0 square root of 3 straight x end root minus square root of 8 straight y end root equals square root of 3 left parenthesis 0 right parenthesis minus square root of 8 left parenthesis 0 right parenthesis equals 0$

This verifies the solution.