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: System 1: 4x + 5y &= 23 &(1) \\ 2x + 3y &= 13 &(2) Step 1: Multiply Equation (2) by 2 to make the coefficients of x equal. 2 × (2x + 3y) = 2 × 13 4x + 6y = 26 &(3) Step 2: Subtract Equation (1) from Equation (3) to eliminate x. (4x + 6y) - (4x + 5y) = 26 - 23 y = 3 Step 3: Substitute the value of y into Equation (2) to find x. 2x + 3(3) = 13 2x + 9 = 13 2x = 13 - 9 2x = 4 x = 2 The solution for the first system is x=2, y=3. System 2: p + b &= 1200 &(1) \\ 2p + 3b &= 3100 &(2) Step 1: Multiply Equation (1) by 2 to make the coefficients of p equal. 2 × (p + b) = 2 × 1200 2p + 2b = 2400 &(3) Step 2: Subtract Equation (3) from Equation (2) to eliminate p. (2p + 3b) - (2p + 2b) = 3100 - 2400 b = 700 Step 3: Substitute the value of b into Equation (1) to find p. p + 700 = 1200 p = 1200 - 700 p = 500 The solution for the second system is p=500, b=700. Send me the next one 📸