Write as a Vector Equality x+y=7 , y-x=7

Problem

{[x+y=7],[y−x=7])

Solution

1. Rearrange the equations so that the variables x and y are in the same order in both equations.

x+y=7

−x+y=7

2. Identify the coefficients of x and y to form the column vectors for each variable.

Coefficients of *x:([1],[−1])

Coefficients of *y:([1],[1])

3. Identify the constants on the right side of the equations to form the constant vector.

Constants:([7],[7])

4. Construct the vector equality by multiplying each variable by its corresponding coefficient vector and setting their sum equal to the constant vector.

x*([1],[−1])+y*([1],[1])=([7],[7])

Final Answer

x*([1],[−1])+y*([1],[1])=([7],[7])

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