Find the Variables [[x+y,-3],[5,y]]=[[8,-3],[z,6]]

Problem

[[x+y,−3],[5,y]]=[[8,−3],[z,6]]

Solution

1. Equate corresponding elements from the matrices to form a system of equations.

x+y=8

−3=−3

5=z

y=6

2. Identify the values for y and z directly from the equations.

y=6

z=5

3. Substitute the value of y into the first equation to solve for x

x+6=8

4. Solve for x by subtracting 6 from both sides.

x=2

Final Answer

x=2,y=6,z=5

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