Write as a Vector Equality x+2y=4 , 2y=-x+4

Problem

x+2*y=4,2*y=−x+4

Solution

1. Identify the system of linear equations. Both equations represent the same line, as the second equation 2*y=−x+4 is equivalent to x+2*y=4 when rearranged.

2. Solve for one variable in terms of the other to find the general solution. Let y=t where t is a scalar parameter.

3. Substitute y=t into the equation x+2*y=4 to find x=4−2*t

4. Express the solution as a vector ([x],[y]) by separating the constant terms from the terms containing the parameter t

5. Write the vector equality in the form r=p+t*v where p is a position vector and v is the direction vector.

Final Answer

([x],[y])=([4],[0])+t*([−2],[1])

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