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
Here are the solutions for the systems of equations: Problem 2: We have the system: 3x - 2y = 8 &(1) \\ x + y = 5 &(2) Step 1: Express x in terms of y from equation (2). x = 5 - y Step 2: Substitute this expression for x into equation (1). 3(5 - y) - 2y = 8 15 - 3y - 2y = 8 15 - 5y = 8 Step 3: Solve for y. -5y = 8 - 15 -5y = -7 y = (-7)/(-5) y = (7)/(5) Step 4: Substitute the value of y back into the expression for x. x = 5 - (7)/(5) x = (25)/(5) - (7)/(5) x = (18)/(5) The solution for problem 2 is: x = (18)/(5), y = (7)/(5) Problem 3: We have the system: 4x - 3y = -13 &(1) \\ x - 5y = 1 &(2) Your previous work showed y=3, which is incorrect. Let's solve it step-by-step. Step 1: Express x in terms of y from equation (2). x = 1 + 5y Step 2: Substitute this expression for x into equation (1). 4(1 + 5y) - 3y = -13 4 + 20y - 3y = -13 4 + 17y = -13 Step 3: Solve for y. 17y = -13 - 4 17y = -17 y = (-17)/(17) y = -1 Step 4: Substitute the value of y back into the expression for x. x = 1 + 5(-1) x = 1 - 5 x = -4 The solution for problem 3 is: x = -4, y = -1 Send me the next one 📸