Write as a Vector Equality (2x+3)/(3y-2)=1 , x(2y-5)-2y(x+3)=2x+1

Problem

{[(2*x+3)/(3*y−2)=1],[x*(2*y−5)−2*y*(x+3)=2*x+1])

Solution

1. Simplify the first equation by multiplying both sides by the denominator 3*y−2

2*x+3=3*y−2

2*x−3*y=−5

2. Simplify the second equation by expanding the products and combining like terms.

2*x*y−5*x−2*x*y−6*y=2*x+1

−5*x−6*y=2*x+1

−7*x−6*y=1

3. Identify the coefficients of x and y to form the matrix A and the constants to form the vector b

A=([2,−3],[−7,−6])

b=([−5],[1])

4. Construct the vector equality in the form A*x=b

([2,−3],[−7,−6])*([x],[y])=([−5],[1])

Final Answer

([2,−3],[−7,−6])*([x],[y])=([−5],[1])

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