Mathematics, 10.10.2019 01:30 angellove1707

Solve the system of equations 4x+3y+6z=3, 5x+5y+6z=5 and 6x+3y+6z=3

Answers: 2

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Answer from: prettyswagg63oz3tyz

Hello!

The answer is:

The solutions to the system of equations are:

$x=0\\y=1\\z=0$

Why?

To solve the system of equations by the easiest way, we need to use the reduction method. The reduction method consist of reducing the variables applying different math operations in order to be able to isolate the variables.

So, we are given the system:

$4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3$

Let's work with the first and the third equation:

$4x+3y+6z=3\\6x+3y+6z=3$

Then, multiplying the first equation by -1, we have:

$-4x-3y-6z=-3\\6x+3y+6z=3$

-4x+6x-3y+3y-6z+6z=-3+3

2x=0

x=0

Now, working with the first and the second equation, we have:

$4x+3y+6z=3\\5x+5y+6z=5$

Then, multiplying the first equation by -1, we have:

$-4x-3y-6z=-3\\5x+5y+6z=5$

5x-4x+5y-3y-6z+6z=-3+5

x+2y=2

Then, substituting "x" into the equation, we have:

0+2y=2

$y=\frac{2}{2}=1$

Finally, working with the first equation and substituting "x" and "y", we have:

4x+3y+6z=3

4*0+3*1+6z=3

0+3+6z=3

6z=3-3=0

6z=0

$z=\frac{0}{6}=0$

Hence, we have that the solutions to the system of equations are:

$x=0\\y=1\\z=0$

Have a nice day!

Answer from: winstonbendariovvygn

$x=0\\y=1\\z=0$

Step-by-step explanation:

Multiply the first equation by -1:

$(-1)(4x+3y+6z)=3(-1)\\\\-4x-3y-6z=-3$

Add the new equation and the third equation an solve for "x":

$\left \{ {{-4x-3y-6z=-3\ \atop {6x+3y+6z=3} \right.\\...........................\\2x=0\\x=0$

Substitute the value of "x" into the first equation and solve for "y":

$4(0)+3y+6z=3\\\\3y=3-6z\\\\y=\frac{3-6z}{3}\\\\y=1-2z$

Substitute the value of "x" and y=1-2z into the second equation and solve for "z":

$5(0)+5(1-2z)+6z=5\\\\5-10z+6z=5\\\\-4z=0\\\\z=0$

Knowing the values of "x" and "z", you can substitute them into any original equation and solve for "y". Then:

$4(0)+3y+6(0)=3\\\\3y=3\\\\y=\frac{3}{3}\\\\y=1$

Answer from: Quest

step-by-step explanation:

i believe its "c" because all of the other options include a but it could be d because there is a way of financing with cash at certain places but its uncommon.

Answer from: Quest

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

$\frac{ab}{bc} =\frac{ad}{ab}$

now, we can cross multiply

and we get

$ab\timesab=ad\times bc$

$ab^2=ad\times bc$

so, this could be step to prove it

Seth is using the figure shown below to prove pythagorean theorem using triangle similarity: in the

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