Question

If k=[-4/2 6/-3] and m=[2/8 -2/5] what is x when 2x -k = m

Answer 1

It's B on edge 2021

Explanation:

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Answer 2

`k=\left[(-4)/(2),\ (6)/(-3)\right]=[-2,\ -2]\\\\m=\left[(2)/(8),\ (-2)/(5)\right]=\left[(1)/(4),\ -(2)/(5)\right]\\\\x=[a,\ b]\\\\2x-k=m.\ \text{Substitute:}\\\\2[a,\ b]-[-2,\ -2]=\left[(1)/(4),\ -(2)/(5)\right]\\\\\ [2a,\ 2b]-[-2,\ -2]=\left[(1)/(4),\ -(2)/(5)\right]\\\\\ [2a-(-2),\ 2b-(-2)]=\left[(1)/(4),\ -(2)/(5)\right]\\\\\ [2a+2,\ 2b+2]=\left[(1)/(4),\ -(2)/(5)\right]\iff2a+2=(1)/(4)\ \wedge\ 2b+2=-(2)/(5)`

`2a+2=(1)/(4)\qquad\text{subtract 2 from both sides}\\\\2a=(1)/(4)-2\\\\2a=(1)/(4)-(8)/(4)\\\\2a=-(7)/(4)\qquad\text{divide both sides by 2}\\\\\boxed{a=-(7)/(8)}\\\\2b+2=-(2)/(5)\qquad\text{subtract 2 from both sides}\\\\2b=-(2)/(5)-2\\\\2b=-(2)/(5)-(10)/(5)\\\\2b=-(12)/(5)\qquad\text{divide both sides by 2}\\\\\boxed{b=-(6)/(5)}\\\\Answer:\ \boxed{x=\left[-(7)/(8),\ -(6)/(5)\right]}`