Write as a Vector Equality 3x=4y+8 , 6x=7-5y

Problem

{[3*x=4*y+8],[6*x=7−5*y])

Solution

1. Rearrange the equations into standard form a*x+b*y=c by moving all variable terms to the left side and constant terms to the right side.

3*x−4*y=8

6*x+5*y=7

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

Vector for *x=([3],[6])

Vector for *y=([−4],[5])

3. Express the system as a linear combination of these column vectors equated to the constant vector.

x*([3],[6])+y*([−4],[5])=([8],[7])

Final Answer

x*([3],[6])+y*([−4],[5])=([8],[7])

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