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
You're on a roll — Step 1: Rearrange the given equations into the standard form Ax + By = C. The given system of equations is: 2y + 3x = 7 3x + 2y = 7 (1) 4x + 3y = 15 (2) Step 2: Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of y equal. Multiply equation (1) by 3: 3(3x + 2y) = 3(7) 9x + 6y = 21 (3) Multiply equation (2) by 2: 2(4x + 3y) = 2(15) 8x + 6y = 30 (4) Step 3: Subtract equation (3) from equation (4) to eliminate y. (8x + 6y) - (9x + 6y) = 30 - 21 8x - 9x + 6y - 6y = 9 -x = 9 Step 4: Solve for x. x = -9 Step 5: Substitute the value of x into equation (1) to solve for y. 3(-9) + 2y = 7 -27 + 2y = 7 Step 6: Solve for y. 2y = 7 + 27 2y = 34 y = (34)/(2) y = 17 The solution to the system of equations is: x=-9, y=17 What's next?