Linear Equations in Two Variables (Class 9 Mathematics)
Linear equations in two variables represent straight lines on a coordinate plane. Understanding solutions, graphing, and simultaneous equations is essentia
TL;DR: Linear equations in two variables represent straight lines on a coordinate plane. Understanding solutions, graphing, and simultaneous equations is ess…
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Linear equations in two variables represent straight lines on a coordinate plane. Understanding solutions, graphing, and simultaneous equations is essentia
Linear Equations in Two Variables MCQs with Answers & Explanations
Q1. A linear equation in two variables has the general form:
- ax + by + c = 0 ✓ (correct)
- ax² + bx + c = 0
- ax² + by² + c = 0
- ax/b + c/y = 0
Explanation: The general form is ax + by + c = 0, where a and b are not both zero.
Q2. The solution of a linear equation in two variables is:
- Only integer pairs
- Ordered pair(s) that satisfy the equation ✓ (correct)
- A single point
- A straight line
Explanation: The solution is any ordered pair (x, y) that satisfies the equation; graphically, these form a straight line.
Q3. The equation of the x-axis is:
- x = 0
- x + y = 0
- y = 0 ✓ (correct)
- x = y
Explanation: The x-axis has the equation y = 0, where all points have zero y-coordinate.
Q4. The slope of the line 2x + 3y = 6 is:
- 2/3
- -3/2
- 3/2
- -2/3 ✓ (correct)
Explanation: Rewriting as y = (-2/3)x + 2, the slope is -2/3 (coefficient of x in slope-intercept form).
Q5. Two equations 2x + 3y = 6 and 4x + 6y = 12 represent:
- The same line ✓ (correct)
- Intersecting lines
- Parallel lines
- Perpendicular lines
Explanation: The second equation is 2 times the first, so they represent the same line (infinitely many solutions).
Q6. If x + y = 5 and x - y = 1, then x = ?
- 1
- 3 ✓ (correct)
- 2
- 4
Explanation: Adding the equations: 2x = 6, so x = 3. (Check: 3 + y = 5 gives y = 2; 3 - 2 = 1 ✓)
Q7. The point of intersection of x = 2 and y = 3 is:
- (0, 0)
- (3, 2)
- (2, 3) ✓ (correct)
- (1, 1)
Explanation: The line x = 2 (vertical) and y = 3 (horizontal) intersect at the point (2, 3).
Q8. Which ordered pair is a solution of 2x - 3y = 1?
- (1, 1)
- (1, 1/3)
- (0, 0)
- (2, 1) ✓ (correct)
Explanation: Checking (2, 1): 2(2) - 3(1) = 4 - 3 = 1 ✓
Q9. Two lines are parallel if their slopes are:
- Equal ✓ (correct)
- Negative reciprocals
- Reciprocals
- Opposite
Explanation: Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals.
Q10. The y-intercept of the line 3x + 2y = 6 is:
- 6
- 3 ✓ (correct)
- 3/2
- 2
Explanation: The y-intercept is the value of y when x = 0: 2y = 6, so y = 3.
Frequently Asked Questions
What are the three methods to solve a system of linear equations in two variables?
The three main methods are: (1) Substitution method, where you solve one equation for a variable and substitute into the other; (2) Elimination method, where you add or subtract equations to eliminate a variable; (3) Graphical method, where you plot both lines and find their intersection point.
When does a system of linear equations have no solution?
A system has no solution when the two equations represent parallel lines (same slope but different y-intercepts). In this case, the lines never intersect and there are no common ordered pairs satisfying both equations.
More Class 9 Mathematics MCQs
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