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

Problem

{[y=−2*x+5],[3*x−2*y=4])

Solution

1. Rearrange the first equation into standard form A*x+B*y=C by adding 2*x to both sides.

2*x+y=5

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

3*x−2*y=4

3. Express the system as a linear combination of vectors by separating the terms containing x and the terms containing y

x*[[2],[3]]+y*[[1],[−2]]=[[5],[4]]

4. Rewrite the system in matrix-vector form A*x=b by placing the coefficients into a 2×2 matrix and the variables into a column vector.

[[2,1],[3,−2]]*[[x],[y]]=[[5],[4]]

Final Answer

[[2,1],[3,−2]]*[[x],[y]]=[[5],[4]]

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