Write as a Vector Equality 6x+3y=6 , y=2x-4 , y=-2x+6

Problem

6*x+3*y=6,y=2*x−4,y=−2*x+6

Solution

1. Rewrite each equation in the standard form a*x+b*y=c to align the variables.

6*x+3*y=6

−2*x+y=−4

2*x+y=6

2. Identify the coefficients of x and y to form the column vectors for the vector equation.

Vector for *x:([6],[−2],[2])

Vector for *y:([3],[1],[1])

3. Identify the constants on the right side of the equations to form the result vector.

Constant vector:([6],[−4],[6])

4. Construct the vector equality by multiplying the variable scalars by their respective coefficient vectors and setting them equal to the constant vector.

x*([6],[−2],[2])+y*([3],[1],[1])=([6],[−4],[6])

Final Answer

x*([6],[−2],[2])+y*([3],[1],[1])=([6],[−4],[6])

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