This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the coefficients of the given system of linear equations. The given system of equations is: 2x + ay = 1 3x - 5y = 7 Comparing these with the standard form a_1x + b_1y = c_1 and a_2x + b_2y = c_2, we have: a_1 = 2, b_1 = a a_2 = 3, b_2 = -5 Step 2: Apply the condition for a unique solution. For a system of linear equations to have a unique solution, the ratio of the coefficients of x must not be equal to the ratio of the coefficients of y. (a_1)/(a_2) ≠ (b_1)/(b_2) Step 3: Substitute the coefficients and solve for a. Substitute the values from Step 1 into the condition from Step 2: (2)/(3) ≠ (a)/(-5) To solve for a, multiply both sides of the inequality by -5: -5 × (2)/(3) ≠ a -(10)/(3) ≠ a Step 4: Compare the result with the given options. The condition for a unique solution is a ≠ -(10)/(3). Looking at the options: (a) a = (10)/(3) (b) a ≠ -(10)/(3) (c) a = 10 (d) a ≠ 10 The correct option is (b). The final answer is (b) a ≠ -(10)/(3). Send me the next one 📸