Solving a System of Linear Equations Using Matrix Multiplication

Math Problem Statement

Jika diketahui x dan y memenuhi hubungan (2 -3) (x y) = (8 -5), maka nilai x + y = ...

The problem presents a system of linear equations using matrix multiplication:

2 & -3 \\ -1 & 2 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ -5 \end{pmatrix}$$ We can solve this system step by step. First, let's multiply the matrices: 1. For the first row: $$2x - 3y = 8$$ 2. For the second row: $$-x + 2y = -5$$ We now have two equations: 1. $$2x - 3y = 8$$ 2. $$-x + 2y = -5$$ I will solve this system of equations to find $$x$$ and $$y$$.The solution to the system of equations is $$x = 1$$ and $$y = -2$$. Thus, the value of $$x + y = 1 + (-2) = -1$$. Therefore, the answer is **C. -1**. Would you like more details on the solution process or have any other questions? Here are five related questions you can explore: 1. How do you solve systems of linear equations using matrices? 2. What are other methods to solve systems of equations (e.g., substitution, elimination)? 3. How does matrix multiplication work in more general cases? 4. What are some real-world applications of systems of equations in matrices? 5. How do you determine if a system of equations has no solution, one solution, or infinitely many solutions? **Tip:** When solving systems of linear equations, always check if the matrix is invertible. This helps determine if the system has a unique solution.

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Algebra
Systems of Linear Equations
Matrix Multiplication

Matrix multiplication: (a b) (x y) = (ax + by)
System of linear equations derived from matrix multiplication

System of linear equations
Matrix multiplication

Grades 9-12

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