Write as a Vector Equality 4x-8=-18 , x+y=3

Problem

{[4*x−8=−18],[x+y=3])

Solution

1. Rearrange the first equation into standard form by adding 8 to both sides to isolate the variable terms.

4*x=−10

2. Identify the coefficients of the variables x and y in both equations to form the coefficient matrix.

([4,0],[1,1])

3. Define the variable vector and the constant vector from the right-hand side of the equations.

x=([x],[y])

b=([−10],[3])

4. Construct the vector equality by expressing the system as a linear combination of column vectors.

x*([4],[1])+y*([0],[1])=([−10],[3])

Final Answer

x*([4],[1])+y*([0],[1])=([−10],[3])

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