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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)

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

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

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

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

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

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

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

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Short Answer Type

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

x + y = 14
x – y = 4

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37.

Solve the following pair of linear equations by the substitution method

s - t = 3

"<pre

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38.

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

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39.
Solve the following pairs of linear equations by the substitution method.
0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3

0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
The given system of linear equations
0.2x + 0.3y = 1.3 ...(i)
0.4x + 0.5y = 2.3 ...(ii)
From equation (i), we have
0.3y =1.3 - 0.2x

$rightwards double arrow space space space space straight y space equals fraction numerator 1.3 minus 0.2 straight x over denominator 0.3 end fraction space space space space space space space..... left parenthesis iii right parenthesis$
Substituting this value ofy in eqn. (ii) we get

0.4x + 0.5 $open parentheses fraction numerator 1.3 minus 0.2 straight x over denominator 0.3 end fraction close parentheses equals 2.3$

$rightwards double arrow space 0.21 space straight x plus 0.65 minus 0.1 straight x space equals space 0.69 rightwards double arrow 0.12 straight x minus 0.1 straight x minus 0.69 minus 0.65 rightwards double arrow 0.02 straight x equals 0.04 rightwards double arrow space space space space space space straight x equals fraction numerator 0.04 over denominator 0.02 end fraction equals 2$
Substituting this value of x in eqn. (iii), we get

$y equals fraction numerator 1.3 minus 0.2 left parenthesis 2 right parenthesis over denominator 0.3 end fraction space equals fraction numerator 1.3 minus 0.4 over denominator 0.3 end fraction equals fraction numerator 0.9 over denominator 0.3 end fraction equals 3$

Therefore, the solution is x = 2, y = 3,
Verification. Substituting x = 2 and y = 3, we find that both the equations (i) and (ii) are satisfied as shown below :
0.2a + 0.3y = (0.2) (2) + (0.3) (3)
= 0.4 + 0.9 = 1.3
0.4x + 0.5y = (0.4) (2) + (0.5) (3)
= 0.8 + 1.5 = 2.23
This verifies the solution.

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40.

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

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