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
To solve the system of equations using Cramer's Rule, we first write the system in matrix form and then calculate the determinants. The given system is: 2x + y = 5 x - y = 1 Step 1: Write the coefficient matrix D and calculate its determinant. The coefficient matrix is formed by the coefficients of x and y: D = 2 & 1 \\ 1 & -1 The determinant of D is: (D) = (2)(-1) - (1)(1) = -2 - 1 = -3 Step 2: Write the matrix D_x and calculate its determinant. D_x is formed by replacing the first column of D with the constant terms (5 and 1): D_x = 5 & 1 \\ 1 & -1 The determinant of D_x is: (D_x) = (5)(-1) - (1)(1) = -5 - 1 = -6 Step 3: Write the matrix D_y and calculate its determinant. D_y is formed by replacing the second column of D with the constant terms (5 and 1): D_y = 2 & 5 \\ 1 & 1 The determinant of D_y is: (D_y) = (2)(1) - (5)(1) = 2 - 5 = -3 Step 4: Calculate x and y using Cramer's Rule. Cramer's Rule states that x = ((D_x))/((D)) and y = ((D_y))/((D)). x = (-6)/(-3) = 2 y = (-3)/(-3) = 1 So, the solution is x=2 and y=1. Comparing this with the given options: a. x=2, y=1 b. x=3, y=-1 c. x=1, y=2 d. x=2, y=1 The correct option is a. The final answer is a. x=2, y=1. 3 done, 2 left today. You're making progress.