Write as a Vector Equality 3x=-4+10 , 4x+3y=11

Problem

{[3*x=−4+10],[4*x+3*y=11])

Solution

1. Simplify the first equation by combining the constant terms on the right side.

3*x=6

2. Rewrite the system of linear equations so that all variables are aligned on the left side and constants are on the right side.

3*x+0*y=6

4*x+3*y=11

3. Express the system as a linear combination of vectors by separating the coefficients of x and y into distinct column vectors.

x*[[3],[4]]+y*[[0],[3]]=[[6],[11]]

4. Convert the linear combination into a matrix-vector product form, which is the standard vector equality representation A*x=b

[[3,0],[4,3]]*[[x],[y]]=[[6],[11]]

Final Answer

[[3,0],[4,3]]*[[x],[y]]=[[6],[11]]

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