The document Very Short Answer Type Questions- Linear Equations in Two Variables Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**Question 1. Show that x = 1, y = 3 satisfy the linear equation 3x – 4y + 9 = 0.****Solution: **We have 3x – 4y + 9 = 0

Putting x = 1, y = 3, we get

L.H.S. = 3(1) – 4(3) + 9 = 3 – 12 + 9

= 12 – 12 = 0 = R.H.S.

Since, L.H.S. = R.H.S.

∴ x = 1 and y = 3 satisfy the given linear equation.**Question 2. Write whether the following statements are True or False? Justify your answers.****(i) ax + by + c, where a, b and c are real numbers, is a linear equation in two variables. **

**(ii) A linear equation 2x + 3y = 5 has a unique solution. **

**(iii) All the points (2, 0), (–3, 0), (4, 2) and (0, 5) lie on the x-axis.**

**(iv) The line parallel to y-axis at a distance 4 units to the left of y-axis is given by the equation x = –4. **

**(v) The graph of the equation y = mx + c passes through the origin.****Solution. **(i) **False.** [Because ax + by + c = 0 is a linear equation in two variables if both ‘a‘ and ‘b’ are non-zero.]

(ii) **False.** [Because a linear equation in two variables has infinitely many solutions.]

(iii) **False.** [Because the points (2, 0) and (–3, 0) lie on x-axis, (0, 5) lie on y-axis whereas the point (4, 2) lies in the first quadrant.]

(iv) **True.**

(v) **False.** [Because the point (0, 0) i.e., x = 0 + y = 0 does not satisfy the equation]**Question 3. Write whether the following statement is True or False? Justify your answer.The co-ordinates of points given in the table:**

**Represent some of the solutions of the equation 2x + 2 = y.****Solution. **True. [Since, on looking at the given co-ordinates, we observe that each y-coordinate is two units more than double the x-coordinate.]**Question 4. Look at the following graphical representation of an equation. Which of the points (0, 0) (0, 4) or (–1, 4) is a solution of the equation?**

**Solution:** Since, the point (0, 4) lies on the line.

is a solution of the equation.

.

**Question 5. Look at the following graphical representation of an equation. Which of the following is not its solution? **

**Solution: **The point (6, 0) does not lie on the graph.

∴ The point (6, 0) is not the solution of the equation.

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### Short Notes - Linear Equations in Two Variables

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