Write as a Vector Equality 2y=14-6x , 3x+y=7

Problem

{[2*y=14−6*x],[3*x+y=7])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by adding 6*x to both sides.

6*x+2*y=14

2. Identify the coefficients and constants for both equations to prepare for vector notation.

Equation 1: *6*x+2*y=14

Equation 2: *3*x+1*y=7

3. Express the system as a linear combination of vectors by grouping the coefficients of x and y into separate column vectors.

x*[[6],[3]]+y*[[2],[1]]=[[14],[7]]

4. Simplify the vector equation if possible. Notice that the first equation is exactly twice the second equation, meaning the vectors are proportional.

2*(3*x+y)=14⇒3*x+y=7

Final Answer

x*[[6],[3]]+y*[[2],[1]]=[[14],[7]]

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