Find the values of x, y, and λ that satisfy the system of equations. such systems arise in certain problems of calculus, and λ is called the lagrange multiplier. (enter your answers as a comma-separated list. if there is no solution, enter no solution. if the system has an infinite number of solutions, set λ = t and solve for x and y in terms of t.) 4x + λ = 0 4y + λ = 0 x + y − 8 = 0

x=4, y=4, λ=-16

Step-by-step explanation:

We have this 3x3 system of linear equations:

λ

λ

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

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

Swap R1 and R3

R3-4R1

R3+R2

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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step-by-step explanation:

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answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: