Write as a Vector Equality y=-x+4 , x+y=4

Problem

y=−x+4,x+y=4

Solution

1. Rearrange the equations into standard form a*x+b*y=c Both equations represent the same line, as y=−x+4 is equivalent to x+y=4

2. Identify the coefficients of the variables x and y to form the left-hand side of the vector equation.

3. Express the linear combination of variables as a dot product of a coefficient vector and a variable vector.

4. Equate the dot product to the constant term on the right-hand side.

Final Answer

([1],[1])⋅([x],[y])=4

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