Final answer:
To solve the given system of equations using the matrix equation, rewrite the equations in matrix form and find the values of x and y using matrix operations.
Step-by-step explanation:
To solve the given system of equations using the matrix equation, we can rewrite the equations in matrix form as:
[2, 3][x, y] = [23]
[3, -4][x, y] = [-8]
Next, we can write the augmented matrix for the system:
|2, 3| |x| = |23|
|3, -4| |y| = |-8|
Now, we can use matrix operations to find the values of x and y. We can multiply the first row by 3 and the second row by 2 to eliminate the x variable:
|6, 9| |x| = |69|
|6, -8| |y| = |-16|
Next, we can subtract the second row from the first row to eliminate the y variable:
|0, 17| |x| = |85|
|6, -8| |y| = |-16|
Dividing the first row by 17, we get the solution for x:
x = 5
Substituting the value of x into the second equation, we can solve for y:
3(5) - 4y = -8
15 - 4y = -8
-4y = -23
y = -23/-4
y = 5.75
Therefore, the solution to the system of equations is x = 5 and y = 5.75.