Write as a Vector Equality -x-4y=0 , y=-1/4x+1

Problem

−x−4*y=0,y=−1/4*x+1

Solution

1. Analyze the system of equations to determine if they are consistent.

2. Rewrite the first equation in slope-intercept form by solving for y

−x−4*y=0

−4*y=x

y=−1/4*x

3. Compare the two equations. The first equation is y=−1/4*x and the second equation is y=−1/4*x+1

4. Identify that these lines have the same slope but different y-intercepts, meaning they are parallel and never intersect.

5. Conclude that there is no solution to the system, so it cannot be written as a single vector equality representing a point of intersection. However, the task asks to represent the system in vector form x=a+t*v or A*x=b

6. Express the system in the standard matrix-vector form A*x=b

7. Rearrange the second equation into standard form a*x+b*y=c

y=−1/4*x+1

1/4*x+y=1

8. Write the system as a vector equality using the coefficients of x and y

x*[[−1],[1/4]]+y*[[−4],[1]]=[[0],[1]]

Final Answer

x*[[−1],[1/4]]+y*[[−4],[1]]=[[0],[1]]

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