linear equations in two variables class 10
A linear equations in two variables class 10 is an equation of the form ax + by = c, where a, b, and c are real numbers, and x and y are variables. The graph of such an equation is always a straight line. Each solution of the equation corresponds to a point on the line. Since there are infinitely many points on a line, a linear equation in two variables has infinitely many solutions. These equations are used to represent real-life situations involving two quantities. To find the solutions, we often use methods like substitution, elimination, or graphical representation.
Graph of the Linear Equation: x + y = 4
Graphical Notion of Linear Equation in Two Variables
A linear equation in two variables class 10 (such as ax + by = c) represents a straight line when plotted on a graph. The steps to graphically represent such an equation are:
- Convert to y = mx + c form (if needed), where m is the slope and c is the y-intercept.
- Choose any two values of x, calculate the corresponding y-values using the equation.
- Plot the two points (x, y) on the Cartesian plane.
- Draw a straight line passing through both points. This line represents the equation.
Every point on the line is a solution to the equation.
Important 20 questions and answers for linear equations in two variables:(LINEAR EQUATIONS IN TWO VARIABLES:CBSE:CLASS10)
A set of 20 objective-type questions with answers for Class 10 – Chapter: Linear Equations in Two Variables (as per CBSE/NCERT syllabus):
🔢 Objective Questions – Linear Equations in Two Variables (linear equations in two variables class 10)
1. A linear equation in two variables can be represented as:
A) ax + b = 0
B) ax² + by = c
C) ax + by = c
D) None of these
Answer: C) ax + by = c
2. In the equation 3x + 4y = 12, the coefficients of x and y are:
A) 3 and 4
B) 4 and 12
C) 3 and 12
D) x and y
Answer: A) 3 and 4
3. Which of the following is a solution of the equation 2x + 3y = 12?
A) (3,2)
B) (0,4)
C) (6,0)
D) (2,4)
Answer: A) (3,2)
4. The graph of a linear equation in two variables is a:
A) Curve
B) Line
C) Parabola
D) Circle
Answer: B) Line
5. How many solutions does a linear equation in two variables have?
A) One
B) Two
C) Infinite
D) None
Answer: C) Infinite
6. Which of the following is not a linear equation in two variables?
A) x + y = 7
B) x² + y = 5
C) 2x – 3y = 9
D) x + 2y = 0
Answer: B) x² + y = 5
7. What is the value of y in the equation 2x + y = 10, if x = 4?
A) 8
B) 10
C) 2
D) 4
Answer: C) 2
8. The equation y = 5x + 3 is a:
A) Linear equation
B) Quadratic equation
C) Cubic equation
D) Constant equation
Answer: A) Linear equation
9. The graph of the equation x = 3 is a:
A) Horizontal line
B) Vertical line
C) Diagonal line
D) Curved line
Answer: B) Vertical line
10. The graph of the equation y = 2 is a:
A) Vertical line
B) Horizontal line
C) Parabola
D) Slanted line
Answer: B) Horizontal line
11. In the equation x – y = 0, one solution is:
A) (2,1)
B) (1,1)
C) (0,1)
D) (1,0)
Answer: B) (1,1)
12. The equation 5x + 0y = 10 represents a line:
A) Parallel to y-axis
B) Parallel to x-axis
C) Passing through origin
D) None of these
Answer: A) Parallel to y-axis
13. Which of the following pairs (x, y) satisfies the equation x + y = 0?
A) (2, 2)
B) (1, -1)
C) (-2, -2)
D) (0, 1)
Answer: B) (1, -1)
14. The equation x = 0 represents a line:
A) Parallel to y-axis
B) On y-axis
C) Parallel to x-axis
D) On x-axis
Answer: B) On y-axis
15. Which of the following equations is not linear?
A) 3x + 2y = 4
B) x + y = 7
C) xy = 6
D) y = 4x – 3
Answer: C) xy = 6
16. The general form of a linear equation in two variables is:
A) ax + by + c = 0
B) ax² + by + c = 0
C) ax – b = c
D) ax + by = c
Answer: A) ax + by + c = 0
17. Which one is the graph of y = -x?
A) A line with positive slope
B) A horizontal line
C) A vertical line
D) A line with negative slope
Answer: D) A line with negative slope
18. Which of the following is a linear equation in two variables?
A) x + y = 5
B) x² + y² = 25
C) x + y² = 7
D) x² – y = 3
Answer: A) x + y = 5
19. If x = 0 and y = 0 satisfies an equation, it is said to:
A) Be non-linear
B) Pass through origin
C) Have no solution
D) Be a parabola
Answer: B) Pass through origin
20. Which of the following points lies on the line 2x – y = 4?
A) (1,2)
B) (2,0)
C) (3,2)
D) (0,4)
Answer: C) (3,2)
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