Solving systems

Question

solve the system by computing X=A^-1B

 

x+3y=10

-2x+3y=-2

Answer 1

x=10-3y

-2x +3y =-2

-2(10-3y) + 3y =-2

-20 +6y+3y =-2

9y = 18

y = 2

x =4

in matrix form

1 3 10

-2 3 -2

double first row and add to 2nd

1 3 10

0 9 -18

divide 2nd row by 9

1 3 10

0 1 2

multiply 2nd by 3 and subtract from row 1

1 0 4

0 1 2

solution is the last column x=4, y=2