Mark M. answered • 06/11/20

Mathematics Teacher - NCLB Highly Qualified

x = -5 - 3y

Substitute for x in the top two equations.

Eliminate either the y or the z

Determine value of other variable and x.

Amanda M.

asked • 06/11/20x+y+2z=-2

3x-y+14z=6

x+3y=-5

**Please include steps and answer**

please also try to explain how to draw the system

Follow
•
1

Add comment

More

Report

Mark M. answered • 06/11/20

Tutor

5.0
(243)
Mathematics Teacher - NCLB Highly Qualified

x = -5 - 3y

Substitute for x in the top two equations.

Eliminate either the y or the z

Determine value of other variable and x.

Sava D. answered • 06/11/20

Tutor

4.9
(75)
Math master degree tutor with good understanding of precalculus

We will use addition of equations and back substitution to solve the system.

First equation is R1, second equation is R2, third equation is R3.

x + y + 2z = -2 --> R1,

3x - y + 14z = 6 --> R2,

x + 3y = -5 --> R3.

We observe that R3 does not have z, which means coefficient of 0 for z.

We multiply first equation by 7 and subtract the second equation:

7R1 --> 7x + 7y + 14z = -14.

R2 ---> 3x - y + 14z = 6

______________________

4x + 8y = -20.

The system:

x + y + 2z = -2 --> R1,

4x + 8y = -20 --> R2,

x + 3y = -5 --> R3.

We divide R2 by 4. (Note, this makes simply the calculations easier)

R2/4 --> x + 2y = -5.

The system:

x + y + 2z = -2 --> R1,

x + 2y = -5 --> R2,

x + 3y = -5 --> R3.

Now, we simply subtract R3 - R2:

x + 3y = - 5 -->R3

x + 2y = -5 -->R2

y = 0.

We found the variable y. Now, we substitute y in R2 (we can use R3 as well):

x + 2x0 = - 5

We find that x = - 5.

Now, we use R1 to find z:

(-5) + 0 + 2z = -2

and solve for z.

z = 1.5.

You are supposed to check your answers by plugging them in the original equation to verify you did not make a mistake.

As for visualizing solution, it is a point in space.

The three original equations are planes in 3 d coordinate system. They will intersect in a single point with coordinates the solution of the system.

Terri G. answered • 06/11/20

Tutor

5
(7)
Struggling with PreCal? I can help; I've taught it for over 30 years!

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.