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Answer :
Final answer:
The answer provides step-by-step instructions to solve a matrix equation with variables x and y. It explains the process clearly and shows how to find the values of x and y accurately.
Explanation:
Matrix equation: [9183x16]=[92y616]
Given matrix: [9 1; 8 3]x = [9 2; 6 1]y
To find the values of x and y, we need to solve the system of equations formed by the matrix equation.
Step-by-step:
- 9x + 1y = 9
8x + 3y = 2 - Multiply the first equation by 3 and the second equation by 2 to eliminate y: 27x + 3y = 27 and 16x + 6y = 4
- Subtract the two equations: 11x = 23 → x = 2
- Substitute x = 2 into the first equation: 18 + y = 9 → y = -9
- Therefore, the values of the variables are x = 2 and y = -9.
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