Question

Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is

inconsistent.
2x-4y= -4
3x+3y= 2
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. The solution is.
(Simplify your answers.)
OB. There are infinitely many solutions. The solution can be written as {(x,y) |x=y is any real number).
(Simplify your answer. Type an expression using y as the variable.)
OC. The system is inconsistent.
Inc

Answer 1

I can help you solve this system of equations using matrices and row operations. We can write the system in a matrix form:

| 2 -4 | |x| |-4|
| 3 3 | × |y| = | 2|

To solve this using row operations, we can first add -1.5 times the first row to the second row to get a zero in the (2,1) entry:

| 2 -4 | |x| |-4|
| 0 9 | × |y| = | 8|

Next, we can multiply the second row by 1/9 to get a leading 1 in the (2,2) entry:

| 2 -4 | |x| |-4|
| 0 1 | × |y| = | 8/9|

Finally, we can add 4 times the second row to the first row to get a zero in the (1,2) entry:

| 2 0 | |x| |8/9 |
| 0 1 | × |y| = |8/9 |

So, the solution is x = 4/3 and y = 8/9. Therefore, the correct choice is A.