Use the matrix tool to solve the system of equations.Choose the correct ordered pair -3x+5y=195x-5y=-5

To solve the system of equations using matrices, we follow these steps:

1. Write the system of equations in matrix form Ax = B, where A is the coefficient matrix, x is the column matrix of variables, and B is the column matrix of constants.

For the given system:

-3x + 5y = 19 5x - 5y = -5

The matrix form will be:

A = | -3 5 | | 5 -5 |

x = | x | | y |

B = | 19 | | -5 |

2. Find the inverse of matrix A (if it exists). To do this, you need to find the determinant of A and then find the matrix of cofactors, take the transpose (adjugate), and divide by the determinant to get A^(-1).

The determinant of A, det(A), is computed as: det(A) = -3*(-5) - 5*5 det(A) = 15 - 25 det(A) = -10

Since the determinant is not zero, A^(-1) exists.

The matrix of cofactors for A (without the division by the determinant yet) is:

| -5 -5 | | -5 -3 |

Then, take the transpose (called the adjugate matrix):

Adjugate of A = | -5 -5 | | -5 -3 |

Now we divide by the determinant to get A^(-1):

A^(-1) = (1/det(A)) * Adjugate of A A^(-1) = 1/(-10) * | -5 -5 | | -5 -3 |

A^(-1) = | 0.5 0.5 | | 0.5 0.3 |

3. Multiply matrix A^(-1) by matrix B to solve for x.

| 0.5 0.5 | * | 19 | = | 0.5*19 + 0.5*(-5) | | 0.5 0.3 | | -5 | | 0.5*19 + 0.3*(-5) |

| 0.5*19 + 0.5*(-5) | = | 9.5 - 2.5 | | 0.5*19 + 0.3*(-5) | | 9.5 - 1.5 |

The solution: x = 7 y = 8

So, the correct ordered pair that solves the system of equations is (7,8).