Write as a Vector Equality 4x+2y=-6 , y=-2x-3

Problem

4*x+2*y=−6,y=−2*x−3

Solution

1. Identify the system of linear equations provided in the task.

4*x+2*y=−6

y=−2*x−3

2. Rearrange the second equation into standard form a*x+b*y=c to align the variables.

2*x+y=−3

3. Express the system as a linear combination of constant vectors multiplied by the variables x and y

x*[[4],[2]]+y*[[2],[1]]=[[−6],[−3]]

4. Verify the vector equality by checking if the components match the original equations.

4*x+2*y=−6

2*x+y=−3

Final Answer

x*[[4],[2]]+y*[[2],[1]]=[[−6],[−3]]

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