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Solve the system using the matrix equation.
2x+3y=23
3x-4y=-8

User Mum
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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.

User Jason Olson
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