Find the Variables [[6x],[25]]=[[-9],[5y]]

Problem

[[6*x],[25]]=[[−9],[5*y]]

Solution

1. Equate the corresponding elements from the first row of the vectors to form a linear equation for x

6*x=−9

2. Solve for x by dividing both sides of the equation by 6

x=(−9)/6

3. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 3

x=−3/2

4. Equate the corresponding elements from the second row of the vectors to form a linear equation for y

25=5*y

5. Solve for y by dividing both sides of the equation by 5

y=25/5

6. Simplify the result to find the integer value of y

y=5

Final Answer

[[6*x],[25]]=[[−9],[5*y]]⇒x=−3/2,y=5

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