Find the Variables

Problem

[[16,4,16,4],[−3,13,15,16],[0,2,22,0]]=[[16,4,7*x+2,4],[−3,13,15,8*x],[0,2,3*y−5,0]]

Solution

1. Equate corresponding elements from the matrices to set up equations for the unknown variables.

2. Identify the equation for x using the elements in the first row, third column:

16=7*x+2

3. Solve for x by subtracting 2 from both sides and then dividing by 7:

14=7*x

x=2

4. Verify x using the elements in the second row, fourth column:

16=8*x

x=2

5. Identify the equation for y using the elements in the third row, third column:

22=3*y−5

6. Solve for y by adding 5 to both sides and then dividing by 3:

27=3*y

y=9

Final Answer

x=2,y=9

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