3 years ago

Plz answer quick!!!

Mathematics

1 answer:

erica [24]3 years ago

4 0

75.36 is the answer.

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Find the values of x, y, and λ that satisfy the system of equations. Such systems arise in certain problems of calculus, and λ i

Nimfa-mama [501]

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x=4, y=4, λ=-16

Step-by-step explanation:

We have this 3x3 system of linear equations:

$4x+$ λ $=0$

$4y+$ λ $=0$

$x+y=8$

So, let's rewrite the system in its augmented matrix form

$\left[\begin{array}{cccc}4&0&1&0\\0&4&1&0\\1&1&0&8\end{array}\right]$

Let´s apply row reduction process to its associated augmented matrix:

Swap R1 and R3

$\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\4&0&1&0\end{array}\right]$

R3-4R1

$\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&-4&1&-32\end{array}\right]$

R3+R2

$\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&0&2&-32\end{array}\right]$

Now we have a simplified system:

x+y+0=0

0+4y+λ=0

0+0+2λ=-32

Solving for λ, x, and y

λ=-16

x=4

y=4

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