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 the matrix method, first, write the equations in the standard form ax + by = c: 1) 2x + 3y = 13 2) -3x + 2y = 0 Step 1: Write the system in matrix form AX = B. 2 & 3 \\ -3 & 2 x \\ y = 13 \\ 0 Here, A = 2 & 3 \\ -3 & 2 , X = x \\ y , and B = 13 \\ 0 . Step 2: Calculate the determinant of matrix A. For a 2 × 2 matrix a & b \\ c & d , the determinant is ad - bc. (A) = (2)(2) - (3)(-3) = 4 - (-9) = 4 + 9 = 13 Step 3: Calculate the inverse of matrix A. The inverse of a 2 × 2 matrix is A^-1 = (1)/((A)) d & -b \\ -c & a . A^-1 = (1)/(13) 2 & -3 \\ 3 & 2 Step 4: Multiply A^-1 by B to find X. X = A^-1B x \\ y = (1)/(13) 2 & -3 \\ 3 & 2 13 \\ 0 x \\ y = (1)/(13) (2)(13) + (-3)(0) \\ (3)(13) + (2)(0) x \\ y = (1)/(13) 26 + 0 \\ 39 + 0 x \\ y = (1)/(13) 26 \\ 39 x \\ y = (26)/(13) \\ (39)/(13) x \\ y = 2 \\ 3 Step 5: State the values of x and y. Therefore, x = 2 and y = 3. The solution is: x=2, y=3 Send me the next one 📸