Solving for x and y in a given matrix

Question

How do I solve for x and y in the following:

[2, 1, -3, 2] = [x+3, 1, -3, 3y-4]

(Note: for each determinant, the first two numbers are the top row.)

Answer 1

It would be best to equate each element in both matrices with the same position within each one.

We get 4*1 = 4 equations

1. 2= x+3 that is equivalent to x=-1 (1)

1 = 1 This is satisfied always (2)

-3 = -3. This is always satisfied (3)

2 = 3y-4 This is equivalent to 3y=2+4=6 or and y=6/3=2 (4)

(2) and (3) can be ignored since they are always satisfied. (1) and (4) give a solution x=-1 and y=2

Answer 2

Given Matrix:

[ 2 1 ;−3 2 ]=[ x+3 1; -3 3y−4]

We equate corresponding elements from both matrices:

1. Top left element: 2=x+3

Solving for x:

x=2−3=−1

1. Top right element: 1=1 (this is already satisfied).
2. Bottom left element: −3=−3 (this is already satisfied).
3. Bottom right element: 2=3y−4

Solving for y:

2=3y−4

3y=2+4=6

y = 6/3 = 2

Therefore, the solutions are x=−1 and y=2.

Answer 3

You should solve

x+3=2 and 3y-4=2

That's all.