Write as a Vector Equality 0.05x+0.04y=273 , x=2y

Problem

0.05*x+0.04*y=273,x=2*y

Solution

1. Rearrange the second equation into standard form by moving all variables to the left side.

x−2*y=0

2. Identify the coefficients of the variables x and y from both equations to form the coefficient matrix.

([0.05,0.04],[1,−2])

3. Define the vector of variables and the vector of constants from the right-hand side of the equations.

v=([x],[y])

b=([273],[0])

4. Express the system as a linear combination of column vectors by multiplying each variable by its corresponding column of coefficients.

x*([0.05],[1])+y*([0.04],[−2])=([273],[0])

Final Answer

x*([0.05],[1])+y*([0.04],[−2])=([273],[0])

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