Write as a Vector Equality y=-1/2x-3 , 4x-2y=16

Problem

y=−1/2*x−3,4*x−2*y=16

Solution

1. Rewrite the first equation into standard form A*x+B*y=C by multiplying by 2 to clear the fraction.

2*y=−x−6

x+2*y=−6

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

A=([1,2],[4,−2])

3. Define the vector of variables v and the vector of constants b from the right-hand sides of the equations.

v=([x],[y])

b=([−6],[16])

4. Express the system as a single vector equality in the form x*(a_1)+y*(a_2)=b by using the columns of the coefficient matrix.

x*([1],[4])+y*([2],[−2])=([−6],[16])

Final Answer

x*([1],[4])+y*([2],[−2])=([−6],[16])

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