Math Problem Statement
Jika (-1 5) (x) = (-13) maka x dan y berturut-turut....
(4 -6) (y) (24)
Solution
To solve the problem, let’s rewrite and solve the matrix equation step-by-step.
Problem:
The matrix equation is:
-1 & 5 \\ 4 & -6 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -13 \\ 24 \end{bmatrix}$$ We need to solve for $$x$$ and $$y$$. ### Step 1: Write out the system of linear equations Multiplying the matrices gives: $$\begin{aligned} -1x + 5y &= -13 \quad \text{(Equation 1)} \\ 4x - 6y &= 24 \quad \text{(Equation 2)} \end{aligned}$$ ### Step 2: Solve the equations #### From Equation 1: $$-1x + 5y = -13 \implies x = 5y + 13 \quad \text{(Rearranged for $$x$$)}$$ #### Substitute $$x = 5y + 13$$ into Equation 2: $$4(5y + 13) - 6y = 24$$ Simplify: $$20y + 52 - 6y = 24$$ $$14y + 52 = 24$$ $$14y = -28$$ $$y = -2$$ #### Substitute $$y = -2$$ back into $$x = 5y + 13$$: $$x = 5(-2) + 13$$ $$x = -10 + 13$$ $$x = 3$$ ### Final Answer: $$x = 3, \, y = -2$$ The correct choice is **B. $$3$$ and $$-2$$**. --- Let me know if you want further details or have additional questions! Here are 5 related questions for practice: 1. How would you solve a matrix equation if it included more variables? 2. How can you verify the solution of a matrix equation? 3. What is the determinant of the coefficient matrix, and how does it impact the solution? 4. What are the steps to invert a matrix for solving systems of linear equations? 5. How would you solve this problem using substitution versus elimination methods? **Tip:** Always check the determinant of a matrix before solving—if it’s zero, the system may not have a unique solution.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Equations
Systems of Linear Equations
Formulas
Matrix multiplication
Substitution method for solving equations
Theorems
Properties of matrix multiplication
Solving systems of linear equations
Suitable Grade Level
Grades 10-12