Write as a Vector Equality x=7(y-5) , 4y=3x+5

Problem

{[x=7*(y−5)],[4*y=3*x+5])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by distributing the constant and moving variables to one side.

x=7*y−35

x−7*y=−35

2. Rearrange the second equation into standard form by moving the x term to the left side.

−3*x+4*y=5

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

Coefficients of *x:([1],[−3])

Coefficients of *y:([−7],[4])

Constants:([−35],[5])

4. Construct the vector equality by expressing the system as a linear combination of the column vectors.

x*([1],[−3])+y*([−7],[4])=([−35],[5])

Final Answer

x*([1],[−3])+y*([−7],[4])=([−35],[5])

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