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

Problem

2/5*x+y=−3,y=2/5*x+3

Solution

1. Rearrange the equations into standard form a*x+b*y=c The first equation is already in this form. For the second equation, subtract 2/5*x from both sides.

−2/5*x+y=3

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

A=[[2/5,1],[−2/5,1]]

3. Define the variable vector x and the constant vector b from the right-hand side of the equations.

x=[[x],[y]]

b=[[−3],[3]]

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

[[2/5,1],[−2/5,1]]*[[x],[y]]=[[−3],[3]]

Final Answer

[[2/5,1],[−2/5,1]]*[[x],[y]]=[[−3],[3]]

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