Write as a Vector Equality 3x=-y+10 , 2x+3y=-12

Problem

{[3*x=−y+10],[2*x+3*y=−12])

Solution

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

3*x+y=10

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

x*([3],[2])+y*([1],[3])=([10],[−12])

3. Express the system as a single vector equality using matrix-vector multiplication.

([3,1],[2,3])*([x],[y])=([10],[−12])

Final Answer

([3,1],[2,3])*([x],[y])=([10],[−12])

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