Write as a Vector Equality y=-2x+14 , y=-x+11

Problem

{[y=−2*x+14],[y=−x+11])

Solution

1. Rearrange the equations into standard form a*x+b*y=c so that the variables are on the left side.

2*x+y=14

x+y=11

2. Identify the coefficients of x and y to form the column vectors for each variable.

Vector for *x=([2],[1])

Vector for *y=([1],[1])

3. Express the system as a linear combination of these column vectors equated to the constant vector.

x*([2],[1])+y*([1],[1])=([14],[11])

4. Rewrite in the standard matrix-vector form A*x=b by grouping the coefficients into a 2×2 matrix.

([2,1],[1,1])*([x],[y])=([14],[11])

Final Answer

([2,1],[1,1])*([x],[y])=([14],[11])

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