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 this system of equations. Given equations: 1) 10m + 4n = 14 2) 5m + (n)/(2) = 14 Step 1: Multiply equation (2) by 2 to eliminate the fraction and make the coefficient of m easier to work with. 2(5m + (n)/(2)) = 2(14) 10m + n = 28 (3) Step 2: Subtract equation (3) from equation (1) to eliminate m. (10m + 4n) - (10m + n) = 14 - 28 10m + 4n - 10m - n = -14 3n = -14 n = -(14)/(3) Step 3: Substitute the value of n into equation (3) to solve for m. 10m + (-(14)/(3)) = 28 10m - (14)/(3) = 28 10m = 28 + (14)/(3) 10m = (28 × 3)/(3) + (14)/(3) 10m = (84)/(3) + (14)/(3) 10m = (98)/(3) m = (98)/(3 × 10) m = (98)/(30) m = (49)/(15) The solution is m = (49)/(15), n = -(14)/(3). What's next?