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. Equation (1): 2x + y = 7 Equation (2): 3x - 2y = 3 Step 2: Solve the system of equations for x and y. We will use the elimination method. Multiply Equation (1) by 2 to make the coefficients of y opposites. 2 × (2x + y) = 2 × 7 4x + 2y = 14 (Equation 3) Now, add Equation (3) and Equation (2): (4x + 2y) + (3x - 2y) = 14 + 3 4x + 3x + 2y - 2y = 17 7x = 17 Divide by 7 to find x: x = (17)/(7) Substitute the value of x into Equation (1) to find y: 2((17)/(7)) + y = 7 (34)/(7) + y = 7 Subtract (34)/(7) from both sides: y = 7 - (34)/(7) y = (49)/(7) - (34)/(7) y = (15)/(7) Step 3: Calculate 7x. We found x = (17)/(7). 7x = 7 × (17)/(7) 7x = 17 Step 4: Determine how much 7x is greater than 10. To find how much 7x is greater than 10, we subtract 10 from 7x. 7x - 10 = 17 - 10 7x - 10 = 7 The value of 7x is greater than 10 by 7. The final answer is 7.