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: Write down the given system of equations. We have the following system: 2x + 2y = 10 (1) 3x - y = 3 (2) Step 2: Multiply equation (2) by 2 to make the coefficients of y opposites. Multiplying equation (2) by 2 gives: 2(3x - y) = 2(3) 6x - 2y = 6 (3) Step 3: Add equation (1) and equation (3) to eliminate y and solve for x. (2x + 2y) + (6x - 2y) = 10 + 6 2x + 6x + 2y - 2y = 16 8x = 16 Divide both sides by 8: (8x)/(8) = (16)/(8) x = 2 Step 4: Substitute the value of x into one of the original equations to solve for y. Using equation (2): 3x - y = 3 Substitute x = 2: 3(2) - y = 3 6 - y = 3 Subtract 6 from both sides: -y = 3 - 6 -y = -3 Multiply both sides by -1: y = 3 The solution to the system of equations is: x = 2 y = 3 Send me the next one 📸