Write as a Vector Equality 12x+5y+6=0 , (5x)/3-(7y)/6=-12

Problem

{[12*x+5*y+6=0],[(5*x)/3−(7*y)/6=−12])

Solution

1. Rearrange the first equation into the standard form a*x+b*y=c by moving the constant term to the right side.

12*x+5*y=−6

2. Clear fractions in the second equation by multiplying every term by the least common multiple of the denominators, which is 6

6⋅(5*x)/3−6⋅(7*y)/6=6⋅(−12)

10*x−7*y=−72

3. Identify the coefficients of the variables x and y to form the coefficient matrix and the constants to form the result vector.

Coefficients of *x:12,10

Coefficients of *y:5,−7

Constants:−6,−72

4. Construct the vector equality by expressing the system as a linear combination of two vectors scaled by the variables x and y

x*[[12],[10]]+y*[[5],[−7]]=[[−6],[−72]]

Final Answer

x*[[12],[10]]+y*[[5],[−7]]=[[−6],[−72]]

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