Matrices Q/A 4: Solving Simultaneous Equations Using the Matrix Method | Step-by-Step Guide

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Hello everyone,
It’s another beautiful day with Mathematics! Still on the topic of matrices, today I’ll be walking you through how to solve a simultaneous linear equation using the matrix method.

To begin with, the first step is to extract the coefficient matrix from the given equations. This is what I refer to as Matrix A. Next, we create Matrix X, which contains the unknown variables (x and y) that we are solving for. Lastly, we form Matrix B, which holds the constants from the equations.

Once we have these three matrices in place, solving for x and y becomes straightforward using the formula:
X = A⁻¹B
We then calculate the inverse of Matrix A, using the formula:
A⁻¹ = 1/det(A) × Adj(A)

After obtaining the inverse, we substitute Matrix B and A⁻¹ into the expression to find Matrix X. This gives us the real values of x and y as 29/13 and 37/13, respectively.

Finally, we verified the solution by substituting the values of x and y back into the original equations, and the results confirmed our answers.

See the step-by-step workings on the google white board below;

Thanks for stopping by my blog, and I hope you found this lesson insightful and educational!

Tools Used

Graphics tablet/Pen
Miro online white board
Laptop

Video edited with VSDC

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