Write as a Vector Equality -4x+2y=-10 , y=2x-5

Problem

−4*x+2*y=−10,y=2*x−5

Solution

1. Rearrange the equations into standard form a*x+b*y=c The first equation is already −4*x+2*y=−10 For the second equation, subtract 2*x from both sides to get −2*x+y=−5

2. Identify the coefficients of the variables x and y to form the column vectors. The coefficients for x are −4 and −2 The coefficients for y are 2 and 1

3. Express the system as a linear combination of these column vectors. Multiply the xcoefficient vector by x and the ycoefficient vector by y

4. Set the sum of these vectors equal to the vector of constants from the right-hand side of the equations, which are −10 and −5

Final Answer

x*[[−4],[−2]]+y*[[2],[1]]=[[−10],[−5]]

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