Question

How do I solve by using Matrices -9x = -4y - 2 and 8y = 18x - 10?

A) Add the two equations together
B) Subtract the first equation from the second equation
C) Divide both equations by -2
D) Multiply both equations by 2

Answer 1

To solve the given system of equations using matrices, rewrite the system in standard form, represent with matrix notation, and solve by finding the inverse of the coefficient matrix and multiplying it with the constants matrix.

Step-by-step explanation:

To solve the system of equations using matrices, none of the options A to D specifically apply to the process of solving with matrices. Instead, we want to first write the system in matrix form. The equations given are -9x = -4y - 2 and 8y = 18x - 10. Let's rewrite these equations in standard form:

• 9x + 4y = 2
• -18x + 8y = 10

Now, we can represent this system as:

• Ax = B, where
• A is the coefficient matrix, x is the variable matrix, and B is the constants matrix.

We then have:

• A = [[9, 4], [-18, 8]]
• x = [[x], [y]]
• B = [[2], [10]]

Next, we compute the inverse of A (if it exists) and then multiply it by B to find x:

• x = A-1B

This provides us with the values for x and y that solve the system of equations.