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KATRIN_1 [288]
2 years ago
14

7. If (2,- 1) is the solution to the following linear system, what are the values of a and b?

Mathematics
1 answer:
igomit [66]2 years ago
8 0

Answer:

• Considering ax + by = -7

{ \tt{ax + by =  - 7}} \\  \\ { \tt{(a \times 2) + (b \times  - 1) =  - 7}} \\  \\ { \boxed{ \tt{2a - b =  - 7 \:  -  -  - eqn \{1 \}}}}

• make b the subject of eqn{1}

{ \tt{b = 2a + 7 -  -  - eqn \{2 \}}}

• considering 2ax - 3by = 1

{ \tt{2ax - 3by = 1}} \\  \\ { \tt{(2a \times 2) - (3b \times  - 1) = 1}} \\  \\ { \boxed{ \tt{4a + 3b = 1 -  -  -  eqn \{3 \}}}}

• substitute b in eqn{3} with b from eqn{2}

{ \tt{4a + 3(2a + 7) = 1}} \\  \\ { \tt{4a + 6a + 21 = 1}} \\  \\ { \tt{10a =  - 20}} \\  \\ { \boxed{ \boxed{ \tt{ \:  \: a =  - 2  \:  \: }}}}

• find b using eqn{2}

{ \tt{b = 2a + 7}} \\  \\ { \tt{b = (2 \times  - 2) + 7}} \\  \\ { \tt{b  =  - 4 + 7}} \\  \\ { \boxed{ \boxed{ \tt{ \:  \: b = 3 \:  \: }}}}

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Answer:

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c. The absolute minimum is at   x = 3  and the absolute maximum is at  x = -5.

Step-by-step explanation:

(a)

Remember that you need to find the points where

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Therefore you have to solve this equation.

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From that equation you can factor out    20x^2  and you would get

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You can factor that equation as    x^2 +2x -15 = (x+5)(x-3) = 0

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So the critcal points are at

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b.  

Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since

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Then, x = -5   is a maximum and x=3 is a minimum

c.

The absolute minimum is at   x = 3  and the absolute maximum is at  x = -5.

6 0
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Read 2 more answers
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