Answer:To solve for x and y using matrices, we can use the inverse of the coefficient matrix. The coefficient matrix is:
[3 10]
[1 3]
The inverse of this matrix is:
1/(33 - 101) * [ 3 -10 ]
[ -1 3 ]
= 1/9 * [ 3 -10 ]
[ -1 3 ]
= [ 1/3 -10/9 ]
[ -1/9 1/3 ]
Multiplying both sides of the matrix equation by the inverse of the coefficient matrix, we get:
[ x ] [ 1/3 -10/9 ] [ 6 ]
[ y ] = [ -1/9 1/3 ] [ 1 ]
Multiplying the matrices on the right-hand side, we get:
[ x ] [ 1/3 * 6 - 10/9 * 1 ]
[ y ] = [ -1/9 * 6 + 1/3 * 1 ]
Simplifying, we get:
[ x ] [ 2/3 ]
[ y ] = [ -1/9 ]
Therefore, the solution to the system of equations is x = 2/3 and y = -1/9.
Explanation: