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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

139 Views

37.
Solve the following pair of linear equations by the substitution method

s - t = 3

We have
s - t = 3

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The given pair of linear equation is
s - t = 3    ...(i)
2s + 3t = 36    ...(ii)
From equation (i), we have
s = 3 + t    ...(iii)

Substitute this value of s in equation (ii), we get
2s + 3t = 36
⇐ 2(3 + t) + 3t = 36
⇒ 6 + 2t + 3t = 36
⇒ 5t + 6 = 36
⇒ 5t = 30
⇒ t = 6
Therefore, the solution is
s = 9, t =6
$straight s over 3 plus straight t over 2 equals 9 over 3 plus 6 over 2 equals 3 plus 3 equals 6$
This verifies the solution.

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

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40.

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

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