LINEAR EQUATIONS IN TWO VARIABLES - MCQs

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Maths — LINEAR EQUATIONS IN TWO VARIABLES

50 Questions Class 9 MCQs
1
A linear equation in two variables represents a
2
The general form of a linear equation in two variables is
3
In the equation \(2x + 3y = 6\), the coefficient of \(y\) is
4
Which of the following is a linear equation in two variables?
5
The equation \(y = 0\) represents
6
The equation \(x = 0\) represents
7
How many solutions can a linear equation in two variables have?
8
The coordinates (0, 3) satisfy which of the following equations?
9
If \(x = 2\), \(y = 3\) satisfy \(2x + 3y = k\), then\( k =\)
10
Which of the following points lies on the line \(x + y = 4\)?
11
The graph of \(x = 5\) is
12
The graph of \(y = 2\) is
13
In \(ax + by + c = 0\), if \(a = 0\), the equation becomes
14
In \(ax + by + c = 0\), if \(b = 0\), the equation represents
15
The pair \((x, y)\) satisfying \(y = 3x\) is
16
The graph of \(y = x\) passes through
17
If (2, 3) is a solution of \(3x + ky = 12\), find \(k\).
18
The \(x\)-intercept of \(2x + 3y = 6\) is
19
The \(y\)-intercept of \(2x + 3y = 6\) is
20
The equation of \(x\)-axis is
21
The equation of \(y\)-axis is
22
The point (–1, 0) lies on
23
The point (0, 4) lies on
24
The slope of line \(y = x\) is
25
If \(x = 2\) and \(y = 3\) satisfy \(ax + by = 12\), then \(2a + 3b\) =
26
Which of the following equations represents a line parallel to \(y\)-axis?
27
Which of the following equations represents a line parallel to \(x\)-axis?
28
If the graph of an equation passes through (0, 0), the equation is
29
In equation \(2x + 3y = 12\), if \(y = 0\), then \(x =\)
30
Which of the following is NOT a linear equation in two variables?
31
The equation \(y = 2x + 1\) cuts the \(y\)-axis at
32
The point where the line crosses the \(x\)-axis has
33
The line \(3x + 2y = 12\) meets\( x\)-axis at
34
The line \(3x + 2y = 12\) meets \(y\)-axis at
35
In the equation \(ax + by + c = 0\), the constants \(a\) and \(b\) cannot be
36
Equation of a line passing through (0, 2) and parallel to \(x\)-axis is
37
Equation of line passing through (3, 0) and parallel to\( y\)-axis is
38
The equation \(0x + y = 4\) represents
39
The equation \(x + 0y = 5\) represents
40
Which of the following points does NOT lie on \(y = 2x\)?
41
Which of these represents a family of lines passing through origin?
42
If \(x = 2\), \(y = 1\) satisfy \(3x – 2y = k\), then \( k =\)
43
Which of the following is the equation of \(x\)-axis?
44
The equation of the line passing through (0, 0) and (2, 2) is
45
The equation \(4x + 2y = 8\) is equivalent to
46
The point (0, 0) satisfies the equation
47
The equation \(3x – 5y + 7 = 0\) has slope
48
The line \(y = –x\) passes through
49
The graph of \(x + y = 0\) passes through
50
The line \(y = 3x + 2\) cuts the \( y\)-axis at
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Frequently Asked Questions

A linear equation in two variables is an equation that can be written in the form ax+by+c=0, where a and b are real numbers, and a and b are not both zero.

Key topics include forming linear equations, representing them graphically, finding solutions, and understanding methods like substitution, elimination, and cross multiplication.

The standard form is ax + by + c = 0.

The coefficients ‘a’ and ‘b’ determine the slope and orientation of the straight line on the Cartesian plane.

It has infinitely many solutions, each corresponding to a point on its straight-line graph.

It is represented by a straight line on the Cartesian plane, showing all possible (x, y) solutions.

Examples include x+y=5, 2x-3y=7, and 4x+y=9.

Only if the constant term c=0; otherwise, (0, 0) may not satisfy the equation.

A one-variable equation has a single solution represented by a point on the number line, while a two-variable equation has infinite solutions represented by a line.

It refers to all pairs (x,y) that satisfy the equation and make both sides equal.

By choosing different values of x, calculating corresponding y values, plotting those points, and joining them to form a straight line.

It is y=mx+c, where m is the slope of the line andcccis the y-intercept.

It shifts the line horizontally or vertically depending on its value.

They are solved by methods like substitution, elimination, graphical interpretation, or cross multiplication.

Because real-life problems often require solving two related conditions simultaneously, such as profit and cost or speed and time.

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