Write as a Vector Equality 6x-5y=35 , 6x=5y+35

Problem

6*x−5*y=35,6*x=5*y+35

Solution

1. Identify the variables and coefficients in the linear equation. The equation 6*x−5*y=35 involves the variables x and y with coefficients 6 and −5

2. Rearrange the second equation 6*x=5*y+35 into standard form by subtracting 5*y from both sides.

6*x−5*y=35

3. Express the left side of the equation as a dot product of a coefficient vector and a variable vector.

([6],[−5])⋅([x],[y])=35

4. Rewrite the equation as a linear combination of vectors by separating the terms associated with each variable.

x*([6],[0])+y*([0],[−5])=([35],[0])

5. Formulate the standard vector equation form a⋅x=c or the column vector form.

Final Answer

([6],[−5])⋅([x],[y])=35

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