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
Let's solve the system of simultaneous equations for part (b). The given equations are: 7x - 3y = 2 (1) 4x - 5y = -12 (2) Step 1: Multiply equation (1) by 5 and equation (2) by 3 to make the coefficients of y equal. 5 × (7x - 3y) = 5 × 2 35x - 15y = 10 (3) 3 × (4x - 5y) = 3 × (-12) 12x - 15y = -36 (4) Step 2: Subtract equation (4) from equation (3) to eliminate y. (35x - 15y) - (12x - 15y) = 10 - (-36) 35x - 15y - 12x + 15y = 10 + 36 23x = 46 Step 3: Solve for x. x = (46)/(23) x = 2 Step 4: Substitute the value of x into equation (1) to find y. 7(2) - 3y = 2 14 - 3y = 2 -3y = 2 - 14 -3y = -12 Step 5: Solve for y. y = (-12)/(-3) y = 4 The solution is: x=2, y=4 Send me the next one 📸