Write as a Vector Equality 4x+2=5y-3 , y=3x-1

Problem

4*x+2=5*y−3,y=3*x−1

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by moving the variable terms to the left and constants to the right.

4*x−5*y=−5

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

−3*x+y=−1

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

([4,−5],[−3,1])

([−5],[−1])

4. Construct the vector equality by multiplying the coefficient matrix by the vector of variables ([x],[y])

([4,−5],[−3,1])*([x],[y])=([−5],[−1])

Final Answer

([4,−5],[−3,1])*([x],[y])=([−5],[−1])

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