PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - MCQs

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Maths — PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

50 Questions Class 10 MCQs
1
Which of the following is a linear equation in two variables?
2
The graph of a linear equation in two variables is always a:
3
A pair of linear equations represents lines that intersect at one point. The system is:
4
For parallel lines, the system of equations has:
5
For coincident lines, the system has:
6
Condition for unique solution is:
7
The equation \(2x + 3y - 6 = 0\) represents:
8
Which method eliminates one variable directly?
9
In substitution method, we:
10
Cross multiplication method applies only when:
11
The graph of \(3x=3\) is:
12
The graph of \(y = 5\) is:
13
If two equations represent the same line, they are:
14
Two equations with no common solution are called:
15
Which is the standard form of a linear equation?
16
A pair of equations represents intersecting lines if:
17
The solution of a pair of linear equations is:
18
Which is an example of parallel lines?
19
Equation \(3x - 9 = 0\) in two variable form is:
20
Number of solutions of coincident lines is:
21
If \(\frac{a_1}{a_2} = \frac{b_1}{b_2}\)?? but \(\frac{a_1}{a_2} \neq \frac{c_1}{c_2}\)?, lines are:
22
To find the graph of a linear equation, we need:
23
A linear equation in two variables has:
24
Which method is most suitable when one variable is already isolated?
25
The determinant \(D = a_1b_2 - a_2b_1\)? equals 0 when:
26
Pair of equations always represents:
27
Solve: \(x + y = 6\), \(x - y = 2\). The value of \(x\) is:
28
In the equation \(5x + 0y = 10\), the graph is:
29
In elimination, to remove \(x\), we:
30
Lines\(x = 2\) and \(x = 3\) are:
31
Lines \(y = 3\) and \(y = -2\) are:
32
In the equation \(ax + by + c = 0\), the slope is:
33
Graphical solution is:
34
If a pair has one solution, the lines:
35
Solving equations means finding:
36
A solution that satisfies both equations is called:
37
Linear equations represent:
38
Solve by elimination: \(2x + 2y = 10,\ x - y = 1\). Value of \(y\):
39
Equation of a line parallel to \(x = 5\) is:
40
Equation of a line parallel to\(y = 7\) is:
41
If two lines intersect, their slopes are:
42
If lines coincide, slopes are:
43
If equations have no solution, they are:
44
Solve: \(3x + y = 7,\ 3x - y = 5\). Value of \(y\):
45
Solve: \(x + 2y = 8,\ x - y = 2\). Value of \(x\):
46
Determine nature: \(2x + 3y = 6,\ 4x + 6y = 12\).
47
Which of the following is not linear?
48
In pair of equations, number of variables is:
49
If elimination results in \(0 = 0\), then:
50
If elimination results in \(0 = 5\), then:
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Frequently Asked Questions

An equation that can be written in the form \(ax + by + c = 0\), where \(a, b, c\) are real numbers and \(a\) and \(b\) are not both zero.

Two linear equations involving the same variables \(x\) and \(y\) that are solved together to find common solutions.

\(a x + b y + c = 0\), where \(a\), \(b\), \(c\) are constants.

A pair of values \((x, y)\) that satisfies both equations simultaneously.

Two straight lines on a coordinate plane.

(i) One solution, (ii) No solution, (iii) Infinitely many solutions.

When the two lines intersect at exactly one point.

\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)

When the lines are parallel and never intersect.

\(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

When both equations represent the same line (coincident lines).

\(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)

Plotting both equations as lines and finding their point of intersection.

The common solution of both equations.

A pair of equations with at least one solution (unique or infinite).

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