Write as a Vector Equality 5x-4y=7 , x=5-2/3y

Problem

5*x−4*y=7,x=5−2/3*y

Solution

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

x+2/3*y=5

2. Identify the coefficients of x and y from both equations to form the coefficient matrix.

([5,−4],[1,2/3])

3. Define the vector of variables and the vector of constants.

x=([x],[y])

b=([7],[5])

4. Express the system as a single vector equality by multiplying the coefficient matrix by the variable vector.

([5,−4],[1,2/3])*([x],[y])=([7],[5])

Final Answer

([5,−4],[1,2/3])*([x],[y])=([7],[5])

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