Find the Variables

Problem

[[1.05,1.1],[1.05,0.9]]*[[x],[y]]=[[1],[1]]

Solution

1. Write the matrix equation as a system of linear equations by performing matrix multiplication.

1.05*x+1.1*y=1

1.05*x+0.9*y=1

2. Subtract the second equation from the first equation to eliminate the variable x

(1.05*x−1.05*x)+(1.1*y−0.9*y)=1−1

3. Simplify the resulting equation to solve for y

0.2*y=0

y=0

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

1.05*x+1.1*(0)=1

1.05*x=1

5. Divide both sides by 1.05 to isolate x

x=1/1.05

x=100/105

x=20/21

Final Answer

[[x],[y]]=[[20/21],[0]]

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