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

answer

106 emergencies

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3