Linear Equations in Two Variables — Important Questions
Gujarat Board · Class 9 · Mathematics
45 important questions from Linear Equations in Two Variables for Gujarat Board Class 9 Mathematics, with answers.
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Important Questions from Linear Equations in Two Variables
Which of the following are solutions to 2x - y = 3? (Select all correct answers)
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(2, 1), (0, -3), (1, -1)
Check each option by substituting into 2x - y = 3: (2,1): 2(2) - 1 = 4 - 1 = 3 ✓. (0,-3): 2(0) - (-3) = 0 + 3 = 3 ✓. (1,-1): 2(1) - (-1) = 2 + 1 = 3 ✓. (3,2): 2(3) - 2 = 6 - 2 = 4 ≠ 3. (1,2): 2(1) - 2 = 2 - 2 = 0 ≠ 3.
If the cost of a notebook is twice the cost of a pen, and notebook costs ₹x and pen costs ₹y, write the linear equation.
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x = 2y
Given: Cost of notebook = ₹x, Cost of pen = ₹y, Notebook costs twice the pen. Therefore: x = 2 × y, which gives us x = 2y.
Find the value of x when y = 0 in the equation 3x + 4y = 12.
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x = 4
Step 1: Substitute y = 0 into 3x + 4y = 12. Step 2: 3x + 4(0) = 12. Step 3: 3x + 0 = 12. Step 4: 3x = 12. Step 5: Divide by 3: x = 4.
Which of the following equations represent the same line as 2x + 3y = 6?
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4x + 6y = 12
To find equivalent equations, multiply the original equation by a constant. 2x + 3y = 6, multiplied by 2 gives: 4x + 6y = 12. This represents the same line because every solution of the original equation is also a solution of the new equation.
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