Question

PLEASE HELP!!

The matrix equation represents a system of equations.

Solve for x and y using matrices. Show or explain all necessary steps.

Answer 1

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:

Answer 2

The value of x and y in the given matrix equation is - 8 and 3 respectively.

How to calculate the value of x and y?

The value of x and y in the given matrix equation is calculated by applying the following formula as shown below;

`\left[\begin{array}{cc}3&10\\1&3\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right] = \left[\begin{array}{c}6\\1\\\end{array}\right]`

The matrix is simplified as follows;

3x + 10y = 6 ---- (1)

x + 3y = 1 ----- (2)

From equation (2);

x = 1 - 3y ------- (3)

Substitute equation (3) into (1);

3x + 10y = 6

3(1 - 3y) + 10y = 6

3 - 9y + 10y = 6

3 + y = 6

y = 6 - 3

y = 3

The value of x is calculated as;

x = 1 - 3y

x = 1 - 3(3)

x = 1 - 9

x = - 8