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
You're on a roll — here are the solutions for the two systems of equations. First System of Equations: 2x + 3y = 13 (1) 3x + y = 9 (2) Step 1: Express y in terms of x from equation (2). From 3x + y = 9, we can write: y = 9 - 3x Step 2: Substitute this expression for y into equation (1). 2x + 3(9 - 3x) = 13 2x + 27 - 9x = 13 -7x + 27 = 13 Step 3: Solve for x. Subtract 27 from both sides: -7x = 13 - 27 -7x = -14 Divide by -7: x = (-14)/(-7) x = 2 Step 4: Substitute the value of x back into the expression for y. y = 9 - 3(2) y = 9 - 6 y = 3 The solution for the first system is x = 2 and y = 3. --- Second System of Equations: 3x - 5y = 7 (1) 2x + y = 9 (2) Step 1: Express y in terms of x from equation (2). From 2x + y = 9, we can write: y = 9 - 2x Step 2: Substitute this expression for y into equation (1). 3x - 5(9 - 2x) = 7 3x - 45 + 10x = 7 13x - 45 = 7 Step 3: Solve for x. Add 45 to both sides: 13x = 7 + 45 13x = 52 Divide by 13: x = (52)/(13) x = 4 Step 4: Substitute the value of x back into the expression for y. y = 9 - 2(4) y = 9 - 8 y = 1 The solution for the second system is x = 4 and y = 1. What's next?