Write as a Vector Equality -4x-6y=8 , 24y=-16x-32

Problem

−4*x−6*y=8,24*y=−16*x−32

Solution

1. Rearrange the equations into standard form a*x+b*y=c so that the variables x and y are on the left side and the constants are on the right.

−4*x−6*y=8

16*x+24*y=−32

2. Identify the coefficients of x and y to form the coefficient matrix A

A=[[−4,−6],[16,24]]

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

x=[[x],[y]]

b=[[8],[−32]]

4. Construct the vector equality by multiplying the coefficient matrix by the variable vector and setting it equal to the constant vector.

[[−4,−6],[16,24]]*[[x],[y]]=[[8],[−32]]

Final Answer

[[−4,−6],[16,24]]*[[x],[y]]=[[8],[−32]]

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