Solve the simultaneous equation given using matrix method7𝑥 + 9𝑦 = 1−2 + 13𝑦 = −10𝑥

To solve the given simultaneous equation using the matrix method, we can represent the equations in matrix form as:

| 7 9 | | x | | 1 | | -10 13 | * | y | = | -2 |

To solve for x and y, we need to find the inverse of the coefficient matrix and multiply it by the constant matrix. Let's proceed with the steps:

Step 1: Calculate the determinant of the coefficient matrix (7 * 13 - 9 * -10 = 91 + 90 = 181).

Step 2: If the determinant is non-zero (in this case, it is), we can proceed to find the inverse of the coefficient matrix.

Step 3: Calculate the inverse of the coefficient matrix using the formula:

| 13/det -9/det | | -10/det 7/det |

In this case, the inverse of the coefficient matrix is:

| 13/181 -9/181 | | -10/181 7/181 |

Step 4: Multiply the inverse of the coefficient matrix by the constant matrix:

| 13/181 -9/181 | | 1 | | x | | -10/181 7/181 | * | -2 | = | y |

Simplifying the multiplication, we get:

(13/181 * 1) + (-9/181 * -2) = x (-10/181 * 1) + (7/181 * -2) = y

Simplifying further, we find:

13/181 + 18/181 = x -10/181 - 14/181 = y

Combining like terms, we get:

31/181 = x -24/181 = y

Therefore, the solution to the simultaneous equation is x = 31/181 and y = -24/181.