Write as a Vector Equality 15x-10y=5 , 15y=-5+10x

Problem

15*x−10*y=5,15*y=−5+10*x

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 side.

15*x−10*y=5

−10*x+15*y=−5

2. Identify the coefficients of x and y to form the coefficient matrix and the constants to form the constant vector.

Coefficients of *x:[[15],[−10]]

Coefficients of *y:[[−10],[15]]

Constants:[[5],[−5]]

3. Express the system as a linear combination of vectors by multiplying the variable x by the first column vector and the variable y by the second column vector.

x*[[15],[−10]]+y*[[−10],[15]]=[[5],[−5]]

Final Answer

x*[[15],[−10]]+y*[[−10],[15]]=[[5],[−5]]

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