**Exercise 13.1**

**Question 1: Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:**

**(i) -2x + 3y = 12**

**(ii) x – y/2 – 5 = 0**

**(iii) 2x + 3y = 9.35**

**(iv) 3x = -7y**

**(v) 2x + 3 = 0**

**(vi) y – 5 = 0**

**(vii) 4 = 3x**

**(viii) y = x/2**

**Solution:**

**Question 2: Write each of the following as an equation in two variables:**

**(i) 2x = -3**

**(ii) y = 3**

**(iii) 5x = 7/2**

**(iv) y = 3/2x**

**Solution:**

**Question 3: The cost of ball pen is Rs 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.**

**Solution:**

**Exercise 13.2**

**Question 1: Write two solutions for each of the following equations:**

**(i) 3x + 4y = 7**

**(ii) x = 6y**

**(iii) x + πy = 4**

**(iv) 2/3x – y = 4.**

**Solution:**

**Question 2: Write two solutions of the form x = 0, y = a and x = b, y = 0 for each of the following equations:**

**(i) 5x – 2y =10**

**(ii) -4x + 3y =12**

**(iii) 2x + 3y = 24**

**Solution:**

**Question 3: Check which of the following are solutions of the equation 2x – y = 6 and which are not:**

**(i) (3 , 0)**

**(ii) (0 , 6)**

**(iii) (2 , -2)**

**(iv) (√3, 0)**

**(v) (1/2,-5)**

**Solution:**

**Question 4: If x = -1, y = 2 is a solution of the equation 3x + 4y = k, find the value of k.**

**Solution:**

**Question 5: Find the value of λ, if x = –λ and y = 5/2 is a solution of the equation x + 4y – 7 = 0**

**Solution:**

**Question 6: If x = 2α + 1 and y = α - 1 is a solution of the equation 2x – 3y + 5 = 0, find the value of α.**

**Solution:**

**Question 7: If x = 1 and y = 6 is a solution of the equation 8x – ay + a**

^{2}= 0, find the values of a.**Solution:**

^{2}= 0

^{2}= 0

^{2}= 0

^{2}– 6a + 8 = 0

^{2}– 6a + 8 = 0

^{2}– 4a – 2a + 8 = 0

**Exercise 13.3**

**Question 1: Draw the graph of each of the following linear equations in two variables:**

**(i) x + y = 4**

**(ii) x – y = 2**

**(iii) -x + y = 6**

**(iv) y = 2x**

**(v) 3x + 5y = 15**

**(vi) x/2 − y/3 = 2**

**(vii) ((x-2))/3 = y – 3**

**(viii) 2y = -x +1**

**Solution:**

**Question 2: Give the equations of two lines passing through (3, 12). How many more such lines are there, and why?**

**Solution:**

**Question 3: A three-wheeler scooter charges Rs. 15 for first kilometer and Rs. 8 each for every subsequent kilometre. For a distance of x km, an amount of Rs. y is paid. Write the linear equation representing the above information.**

**Solution:**

**Question 4: A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid Rs. 27 for a book kept for seven days. If fixed charges are Rs. x and per day charges are Rs y. Write the linear equation representing the above information.**

**Solution:**

**Question 5: A number is 27 more than the number obtained by reversing its digits. lf its unit’s and ten’s digit are x and y respectively, write the linear equation representing the statement.**

**Solution:**

**Question 6: The Sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten’s digit of the number are x and y respectively, then write the linear equation representing the above statement.**

**Solution:**

**Question 7: Plot the Points (3, 5) and (-1, 3) on a graph paper and verify that the straight line passing through the points, also passes through the point (1, 4).**

**Solution:**

**Question 8: From the choices given below, choose the equations whose graph is given in figure.**

**(i) y = x**

**(ii) x + y = 0**

**(iii) y = 2x**

**(iv) 2 + 3y = 7x**

**Solution:**

**Question 9: From the choices given below, choose the equation whose graph is given fig:**

**(i) y = x + 2**

**(ii) y = x – 2**

**(iii) y = – x + 2**

**(iv) x + 2y = 6**

**Solution:**

**Question 10: If the point (2, -2) lies on the graph of linear equation, 5x + ky = 4, find the value of k.**

**Solution:**

**Exercise 13.4**

**Question 1: Give the geometric representations of the following equations**

**(a) on the number line**

**(b) on the Cartesian plane:**

**(i) x = 2**

**(ii) y + 3 = 0**

**(iii) y = 3**

**(iv) 2x + 9 = 0**

**(v) 3x – 5 = 0**

**Solution:**

**Question 2 : Give the geometrical representation of 2x + 13 = 0 as an equation in**

**(i) one variable**

**(ii) two variables**

**Solution:**

**Exercise VSAQs ........................**

**Question 1: Write the equation representing x-axis.**

**Solution:**

**Question 2: Write the equation representing y-axis.**

**Solution:**

**Question 3: Write the equation of a line passing through the point (0, 4) and parallel to x-axis.**

**Solution:**

**Question 4: Write the equation of a line passing through the point (3, 5) and parallel to x-axis.**

**Solution:**

**Question 5: Write the equation of a line parallel to y-axis and passing through the point (-3, -7)**

**Solution:**