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Test: Linear Equations In Two Variables - 1 - Class 9 MCQ


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25 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Linear Equations In Two Variables - 1

Test: Linear Equations In Two Variables - 1 for Class 9 2024 is part of Mathematics (Maths) Class 9 preparation. The Test: Linear Equations In Two Variables - 1 questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Linear Equations In Two Variables - 1 MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Linear Equations In Two Variables - 1 below.
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Test: Linear Equations In Two Variables - 1 - Question 1

The graph of the linear equation 2x – 3y = 6, cuts the y-axis at the point

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 1

To find where the line (2x - 3y = 6) cuts the y-axis, we set (x = 0) and solve for (y).
- Substituting (x = 0):
(2(0) - 3y = 6)
(-3y = 6)
(y = -2
- Thus, the line cuts the y-axis at (0, -2).

So, the correct answer is C:(0, -2)

Test: Linear Equations In Two Variables - 1 - Question 2

The linear equation 2x + 3y = 6 has

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 2

The linear equation (2x + 3y = 6) can be rewritten in the slope-intercept form (y = mx + b).

- Rearrange to (3y = -2x + 6) and then (y = -\frac{2}{3}x + 2\).
- This is a straight-line equation.
- A straight line has infinitely many points.

Thus, the equation has:

- Infinitely many solutions (C)

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Test: Linear Equations In Two Variables - 1 - Question 3

Solve x + 4y = 14 .....(i)

7x - 3y = 5 ....(ii)

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 3

Solution: From equation (i) x = 14 - 4y ....(iii)

Substitute the value of x in equation (ii)

⇒ 7 (14 - 4y) - 3y = 5

⇒ 98 - 28y - 3y = 5

⇒ 98 - 31y = 5

⇒ 93 = 31y

⇒ y = 93/31

⇒ y = 3

Now substitute value of y in equation (iii)

⇒ 7x - 3 (3) = 5

⇒ 7x - 3 (3) = 5

⇒ 7x = 14

⇒ x = 14/7 = 2

So the solution is x = 2 and y = 3

Test: Linear Equations In Two Variables - 1 - Question 4

A linear equation in two variables has maximum :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 4

A linear equation in two variables has maximum:
C: Infinite solutions
- A linear equation in two variables can be written as \( ax + by = c \).
- This equation represents a straight line on the coordinate plane.
- Every point on this line is a solution to the equation.
- Since there are infinitely many points on a line, there are infinitely many solutions to the equation.

Hence, the correct answer is C: Infinite solutions.

Test: Linear Equations In Two Variables - 1 - Question 5

The solution of the equation x + y = 3, 3x – 2y = 4 is :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 5

Solution:

Substitution Method:

- From the first equation, x + y = 3
- Rearranging, we get y = 3 - x
- Substitute y = 3 - x into the second equation 3x - 2(3 - x) = 4
- Simplify the equation: 3x - 6 + 2x = 4
- Combine like terms: 5x - 6 = 4
- Add 6 to both sides: 5x = 10
- Divide by 5: x = 2
- Substitute x = 2 back into y = 3 - x
- y = 3 - 2 = 1

Therefore, the solution is x = 2, y = 1, which corresponds to option A.

Test: Linear Equations In Two Variables - 1 - Question 6

 What will be the value of k, if the lines given by (5+k)x-3y+15 and (k-1)x-y+19 are parallel?

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 6

Test: Linear Equations In Two Variables - 1 - Question 7

x = 2, y = – 1 is a solution of the line equal to :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 7

To find if ( x = 2, y = -1 ) is a solution for a given equation, substitute these values into each equation:

- A: ( 2(2) + 3(-1) =1 not  5 ) ❌
- B: ( 2 + (-1) = 1 not 5 ) ❌
- C: ( 2 + (-1) = 1 ) ✓
- D: ( 2 - (-1) = 3 not 9 ) ❌

Therefore, option C is the correct answer.

Test: Linear Equations In Two Variables - 1 - Question 8

The equation  =has

Test: Linear Equations In Two Variables - 1 - Question 9

The value of x satisfying the equation x2 + p2 = (q – x)2 is :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 9

Solution : 

The correct option is Option B.

x² + p² = (q + x)²

x² + p² = q² - 2qx + x²

Eliminating x² from both sides,

p² = q² - 2qx

x = q² - p² / 2q

Test: Linear Equations In Two Variables - 1 - Question 10

If x = a, y = b is the solution of the pair of equation x-y = 2 and x+y = 4 then what will be value of a and b       

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 10

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Test: Linear Equations In Two Variables - 1 - Question 11

The point of the form (2a, -a) lies on

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 11

The point (2a, -a) lies on the line 2y + x = 0 because:
- For a point to lie on a line, it must satisfy the equation of the line.
- Substituting the coordinates of the point (2a, -a) into the equation 2y + x = 0 gives 2(-a) + 2a = 0.
- Simplifying the equation further, we get -2a + 2a = 0, which is true.
- Therefore, the point (2a, -a) lies on the line 2y + x = 0.

Test: Linear Equations In Two Variables - 1 - Question 12

The sum of a two digit number and the number obtained by reversing the order of the digits is 187. If the digits differ by 1, then what will be the number?
 

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 12

Answer: c
Explanation: Let the two digit number be 10x+y
The number obtained after reversing the digits will be 10y+x
10x+y+10y+x=187
11x+11y=187
x+y=17     (1)
Also, x-y=1     (2)
Adding (1) and (2)
2x=18
x=9
Substituting in equation (1), 9+y=17
y=8
The number is 89 or 98.

Test: Linear Equations In Two Variables - 1 - Question 13

The point of the form (a,0) lies 

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 13

- The point of the form (a,0) lies on the x-axis because the y-coordinate is always 0 on the x-axis.
- The x-axis is the horizontal line on the Cartesian plane where the y-coordinate is always zero.
- Therefore, the correct answer is A: the x-axis.

Test: Linear Equations In Two Variables - 1 - Question 14

The straight line 2x – 5y = 0 passes through the point :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 14

 

Test: Linear Equations In Two Variables - 1 - Question 15

If x = 1,y = 1 is a solution of equation 9ax + 12ay = 63 then, the value of a is :

Test: Linear Equations In Two Variables - 1 - Question 16

The point of the form (a, -a), where  a ≠ 0, lies on

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 16

Test: Linear Equations In Two Variables - 1 - Question 17

The straight line passing through the points (0, 0), (–1, 1) and (1, – 1) has the equation :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 17

We have to check which straight line given in options, passes through the points (0,0),(−1,1) and (1,−1).
Any point lying on the line satisfies its equation.
Let's take option A,2−x=3y
For point (0,0), LHS =2−0=2, RHS =3(0)=0
LHS ≠ RHS
Hence, the line 2−x=3y does not passes through (0,0). So, no need to check whether other points lies on the line or not.

Test: Linear Equations In Two Variables - 1 - Question 18

Which of the following equations is not linear equation :

Test: Linear Equations In Two Variables - 1 - Question 19

The graph of the linear equation 3x – 2y = 6, cuts the x-axis at the point

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 19

To determine where the graph of the equation (3x - 2y = 6) cuts the x-axis, follow these steps:
- Identify the x-intercept: The x-intercept occurs where (y = 0).
- Tequation becomes 3x - 2(0) = 6.
- Solve for (x): (3x = 6), hence (x = 2).
Therefore, the graph cuts the x-axis at the point (2, 0)

Answer: C: (2, 0)

Test: Linear Equations In Two Variables - 1 - Question 20

The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.       

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 20

Let the ones's digit is y

and ten's digit is x

so, two digit number = 10x + y

and the number formed by interchanged the digits = 10y + x

10x + y + 10y + x = 110

⇒ 11x + 11y = 110

⇒ x + y = 10

⇒ x = 10 - y      ---- (1)

10x + y - 10 = 5(x + y) + 4

⇒ 10x + y - 10 = 5x + 5y + 4

⇒ 10x - 5x + y - 5y = 4 + 10

⇒ 5x - 4y = 14      ---- (2)

5(10 - y) - 4y = 14 (From 1)

⇒ 50 - 5y - 4y = 14

⇒ 50 - 9y = 14

⇒ -9y = 14 - 50

⇒ -9y = - 36

⇒ y = 4

so, x =10 - 4

⇒ x = 6

Two digit number = 10 × 6 + 4

⇒ 64

∴ Two digit number is 64.

Test: Linear Equations In Two Variables - 1 - Question 21

The graph of the equation y = x2 is :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 21

In the graph of y = x2, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point. We can graph a parabola with a different vertex.

Test: Linear Equations In Two Variables - 1 - Question 22

The graph of the lines x + y = 7 and x – y = 3 meet at the point :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 22

x + y = 7 
x – y = 3
adding this two equation
2x = 10
x = 5
so y  = 2 
(5,2)

Test: Linear Equations In Two Variables - 1 - Question 23

The graph of the equation 2x – 3 = 3x – 5 is parallel to :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 23

Parallel to the y-axis:.
- Therefore, the graph of the equation 2x - 3 = 3x - 5 solving this we would get
x=2
 is parallel to the y-axis, which is option B.

Test: Linear Equations In Two Variables - 1 - Question 24

The graph of the line 5x + 3y = 4 cuts y-axis at the point :

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 24

Test: Linear Equations In Two Variables - 1 - Question 25

What will be the nature of the graph lines of the equations 5x-2y+9 and 15x-6y+1?

Detailed Solution for Test: Linear Equations In Two Variables - 1 - Question 25

2. Coincident

  • Coincident Lines: Two lines are coincident if they are exactly the same line, meaning they have the same slope and y-intercept. In other words, they overlap completely.
  • For the given equations:

              

  •  Because the y-intercepts are different, the lines are not coincident.

3. Intersecting

  • Intersecting Lines: Two lines are intersecting if they cross each other at exactly one point. This happens when the lines have different slopes.

4. Perpendicular to Each Other

  • Perpendicular Lines: Two lines are perpendicular if the product of their slopes is −1-1−1. In other words, if the slopes are negative reciprocals of each other.

       

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