#### If the point (−1, 3) is a solution of the equation 4x + sy = −1, then the value of s is ____.

Given (−1, 3) is a solution of the equation 4x + sy = −1 By substituting the point (−1, 3) in 4x + sy = −1, we get 4(−1) + s(3) = −1 ⇒ −4 + 3s = −1 ⇒ 3s = 3 ∴ s = 1

#### If the point (1, 4) is a solution of the equation y = tx + 7, then the value of t is ____.

Given (1, 4) is a solution of the equation y = tx + 7 By substituting the point (1, 4) in y = tx + 7 , we get t (1) + 7 = 4 ⇒ t + 7 = 4 ∴ t = −3

#### If the point (3, 3) is a solution of the equation 3x + ky = 6, then the value of k is ____.

Given (3, 3) is a solution of the equation 3x + ky = 6 By substituting the point (3, 3) in 3x + ky = 6, we get 3(3) + k(3) = 6 ⇒ 9 + 3k = 6 ⇒ 3k = −3 ∴ k = −1

#### The graph of the equation x = a is a straight line parallel toY-axis

The graph of the equation x = a is a straight line parallel to Y-axis

#### If the point (2, 2) is a solution of the equation 2x + ky = 6, then the value of k is ____.

Given (2, 2) is a solution of the equation 2x + ky = 6 By substituting the point (2, 2) in 2x + ky = 6, we get 2(2) + k(2) = 6 ⇒ 4 + 2k = 6 ⇒ 2k = 2 ∴ k = 1

#### x = 3 and y = 5 is a solution of 2x + 5y = 24

Given, 2x + 5y = 24 Substituting x = 3 and y = 5 in the above equation, we get 2(3) + 5(5) = 24 6 + 25 = 24 31 ≠ 24 Hence, x = 3 and y = 5 is not a solution of 2x + 5y = 24

#### If the point (−1, 3) is a solution of the equation y = ax + 6, then the value of a is ____.

Given (−1, 3) is a solution of the equation y = ax + 6 By substituting the point (−1, 3) in y = ax + 6 , we get a (−1) + 6 = 3 ⇒ −a + 6 = 3 ∴ a = 3

#### x = 3 and y = 5 a solution of 5x + 3y = 30.

Given, 5x + 3y = 30 Substituting x = 3 and y = 5 in the above equation, we get 5(3) + 3(5) = 30 15 + 15 = 30 30 = 30 Hence, x = 3 and y = 5 is a solution of 5x + 3y = 30

#### A pineapple is priced at cost Rs 7 and a watermelon cost Rs 5. Stella spends Rs 40 on these fruits. The linear equation which satisfies the given data is ____.

Let the number of pineapples and watermelons purchased be x and y respectively. Cost of x pineapples = Rs 7x Cost of y watermelons = Rs 5y Total cost = Rs 40 Hence, the linear equation which satisfies the given data is 7x + 5y = 40.