Write as a Vector Equality 5x-4y=11 , 3x=y+15

Problem

{[5*x−4*y=11],[3*x=y+15])

Solution

1. Rearrange the second equation into standard form a*x+b*y=c by subtracting y from both sides.

3*x−y=15

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

Coefficients of *x:5,3

Coefficients of *y:−4,−1

Constants:11,15

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

x*[[5],[3]]+y*[[−4],[−1]]=[[11],[15]]

4. Rewrite the linear combination as a single matrix-vector product A*x=b

[[5,−4],[3,−1]]*[[x],[y]]=[[11],[15]]

Final Answer

[[5,−4],[3,−1]]*[[x],[y]]=[[11],[15]]

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