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: Express x in terms of y from the second equation. Given the equations: 3x + 4y = 2 (1) x - y = 5 (2) From equation (2), we can isolate x: x = 5 + y (3) Step 2: Substitute the expression for x from equation (3) into equation (1). 3(5 + y) + 4y = 2 Step 3: Solve the equation for y. 15 + 3y + 4y = 2 15 + 7y = 2 Subtract 15 from both sides: 7y = 2 - 15 7y = -13 Divide by 7: y = -(13)/(7) Step 4: Substitute the value of y back into equation (3) to find x. x = 5 + (-(13)/(7)) x = 5 - (13)/(7) To combine these, find a common denominator: x = (5 × 7)/(7) - (13)/(7) x = (35)/(7) - (13)/(7) x = (35 - 13)/(7) x = (22)/(7) The solution is: x = (22)/(7), y = -(13)/(7) x = (22)/(7), y = -(13)/(7) That's 2 down. 3 left today — send the next one.