Write as a Vector Equality 10x+2y=-6 , y=-5x

Problem

10*x+2*y=−6,y=−5*x

Solution

1. Rearrange the second equation into standard form A*x+B*y=C by adding 5*x to both sides.

5*x+y=0

2. Identify the coefficients of the variables x and y from both equations to form the vectors.

10*x+2*y=−6

5*x+y=0

3. Separate the variables into a linear combination of constant vectors.

x*[[10],[5]]+y*[[2],[1]]=[[−6],[0]]

4. Express the system as a single vector equality by combining the left side into a vector sum.

[[10*x+2*y],[5*x+y]]=[[−6],[0]]

Final Answer

[[10*x+2*y],[5*x+y]]=[[−6],[0]]

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