Write as a Vector Equality x-2y=10 , 1/(2x-2y)=4

Problem

{[x−2*y=10],[1/(2*x−2*y)=4])

Solution

1. Rearrange the second equation to a linear form by taking the reciprocal of both sides.

1/(2*x−2*y)=4⇒2*x−2*y=1/4

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

Equation 1: *1*x−2*y=10

Equation 2: *2*x−2*y=1/4

3. Express the system as a linear combination of vectors by separating the x and y components.

x*[[1],[2]]+y*[[−2],[−2]]=[[10],[1/4]]

4. Rewrite the system in the standard matrix-vector form A*x=b

[[1,−2],[2,−2]]*[[x],[y]]=[[10],[1/4]]

Final Answer

[[1,−2],[2,−2]]*[[x],[y]]=[[10],[1/4]]

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