Question

How do you use the matrix method to solve the system of equations `5x+3y = 3` and `2x-6y=30`?

Answer 1

I got:
`x=3`
`y=-4`

Explanation:

We can try using Cramer's Method:

1) evaluate the determinant of the matrix `A` formed with the coefficients of the unknowns:
`|(5,3),(2,-6)|=(-30-6)=-36`

2) evaluate the determinant of the matrix `A_x` formed with the first column of independent terms and the other with the coefficients of the unknowns:
`|(3,3),(30,-6)|=(-18-90)=-108`
3) find `x` by dividing:
`A_x/A=-108/-36=3`

4) evaluate the determinant of the matrix `A_y` formed with the second column of independent terms and the other with the coefficients of the unknowns:
`|(5,3),(2,30)|=(150-6)=144`
5) find `x` by dividing:
`A_y/A=144/-36=-4`

Answer 2

`x=3`
`y=-4`

Explanation:

`x=A_1/A=(-108)/(-36)=3`
`y=A_2/A=(144)/(-36)=-4`