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

Problem

{[y=2*x+10],[2*x+y=−2])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting 2*x from both sides.

−2*x+y=10

2. Identify the coefficients of x and y from both equations to form the coefficient matrix A

A=([−2,1],[2,1])

3. Define the vector of variables v and the vector of constants b

v=([x],[y])

b=([10],[−2])

4. Construct the vector equality by expressing the system in the form A*v=b

([−2,1],[2,1])*([x],[y])=([10],[−2])

Final Answer

([−2,1],[2,1])*([x],[y])=([10],[−2])

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