Write as a Vector Equality 2x+8y=18 , y=(-x)+6

Problem

{[2*x+8*y=18],[y=−x+6])

Solution

1. Rearrange the second equation into standard form A*x+B*y=C by adding x to both sides.

x+y=6

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

[[2,8],[1,1]]

3. Define the vector of variables and the vector of constants.

v=[[x],[y]]

b=[[18],[6]]

4. Express the system as a linear combination of column vectors by multiplying the variables by their respective coefficient columns.

x*[[2],[1]]+y*[[8],[1]]=[[18],[6]]

Final Answer

x*[[2],[1]]+y*[[8],[1]]=[[18],[6]]

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