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Maths 2 Mark Question

Linear Equations in Two Variables · Maharashtra Board STD 9 (MSBSHSE - English Medium). 8 questions.

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2 Mark Question

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8 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
Solve the following simultaneous equations $:x – 2y – 2 ; x + 2y = 10$
Answer
$x-2 y=-2$
$x+2 y=10 $
Adding I and II
$2 x=8$
$\Rightarrow x=4$
Putting the value of $x$ in (I) we get
$4-2 y=-2$
$\Rightarrow-2 y=-6$
$\Rightarrow y=3$
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Question 22 Marks
Solve the following simultaneous equations $:2x – y = 5 ; 3x + 2y = 11$
Answer
$ 2 x-y=5$
$3 x+2 y=11 $
Multiplying (I) with $2$ we get
$4 x-2 y=10$
Adding (II) with (III)
$ 7 x=21$
$\Rightarrow x=3 $
Putting the value of $x$ in (I) we get
$ 2 \times 3-y=5$
$\Rightarrow 6-y=5$
$\Rightarrow y=1 $
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Question 32 Marks
Solve the following simultaneous equations $:2x + y = -2 ; 3x – y = 7$
Answer
$ 2 x+y=-2$
$3 x-y=7$
Adding (I) and (II)
$5 x=5$
$\Rightarrow x=1 $
Putting the value of $x$ in (I)
$ 2 \times 1+y=-2$
$\Rightarrow 2+y=-2$
$\Rightarrow y=-4 $
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Question 42 Marks
Solve the following simultaneous equations $:x + y = 11 ; 2x – 3y = 7$
Answer
$x+y=11$
$2 x-3 y=7 $
Multiply (I) with $3$
$3 x+3 y=33$
Adding (II) and (III)
$5 \mathrm{x}=40$
$\Rightarrow \mathrm{x}=8$
Putting the value of $x$ in (I)
$8+y=11$
$\Rightarrow y=3$
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Question 52 Marks
Solve the following simultaneous equations $:x – 2y = -1 ; 2x – y = 7$
Answer
$ x-2 y=-1$
$2 x-y=7$
Multiply (I) with $2$
$2 x-4 y=-2$
Subtracting (III) from (II)
$ -3 y=-9$
$\Rightarrow y=3$
Putting the value of $y$ in $(\mathrm{I})$ we get
$x-2 \times 3=-1$
$\Rightarrow x-6=-1$
$\Rightarrow x=5$
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Question 62 Marks
Solve the following simultaneous equations :2x + y = 5 ; 3x – y = 5
Answer
Solve the following simultaneous equations.
2x + y = 5 ; 3x – y = 5
x – 2y = -1 ; 2x – y = 7
x + y = 11 ; 2x – 3y = 7
2x + y = -2 ; 3x – y = 7
2x – y = 5 ; 3x + 2y = 11
x – 2y – 2 ; x + 2y = 10
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Question 72 Marks
Write five solutions of the equation x + y = 1.
Answer
i. x = 1, y = 6
ii. x = -1, y = 8
iii. x = 5, y = 2
iv. x = 0, y = 7
v. x = 10, y = -3
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Question 82 Marks
By using variables x and y form any five linear equations in two variables.
Answer
The general form of a linear equation in two variables x and y is ax + by + c = 0,
where a, b, c are real numbers and a ≠ 0, b ≠ 0.
Five linear equations in two variables are as follows:
i. 3x + 4y – 12 = 0
ii. 3x – 4y + 12 = 0
iii. 5x + 5y – 6 = 0
iv. 7x + 12y – 11 = 0
v. x – y + 5 = 0
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