Write as a Vector Equality y=-3x-18 , 5x-2y=-8

Problem

{[y=−3*x−18],[5*x−2*y=−8])

Solution

1. Rearrange the first equation into standard form A*x+B*y=C by adding 3*x to both sides.

3*x+y=−18

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

([3,1],[5,−2])

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

x=([x],[y])

b=([−18],[−8])

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

x*([3],[5])+y*([1],[−2])=([−18],[−8])

Final Answer

x*([3],[5])+y*([1],[−2])=([−18],[−8])

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