Find the unique solution to this system of equations. Give your answer as a point

Question

04-09-2022
Mathematics

Answered

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Find the unique solution to this system of equations. Give your answer as a point

Sagot :

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sqdancefan sqdancefan · Answer 1 · 2022-09-04T17:54:50-04:00

Answer:

(x, y, z) = (-4, -5, 2)

Step-by-step explanation:

You want the solution to the 3×3 system of equations ...

3x -y -4z = -15
-4x -4y -z = 34
2x +3y +5z = -13

Tools

There are many tools available for solving a system of equations. A typical hand-held graphing calculator offers at least two methods. An online graphing calculator solution is shown in the attachment.

For the attached solution, we defined z in terms of x and y using the second equation. This effectively reduces the system to a 2×2 system, which is easily solved. The same "substitution" method can be used when solving the system by hand.

The graph shows the solution to be (x, y, z) = (-4, -5, 2).

Manual solution

Using z = -4x -4y -34 from the second equation, the system reduces to ...

3x -y -4(-4x -4y -34) = -15

19x +15y = -151

and

2x +3y +5(-4x -4y -34) = -13

-18x -17y = 157

Writing these equations in general form, we have ...

19x +15y +151 = 0
18x +17y +157 = 0

The "cross multiplication method" gives the solution for x and y as ...

D = (19)(17) -(18)(15) = 53

x = (15(157) -17(151))/D = -212/53 = -4

y = (151(18) -157(19))/D = -265/53 = -5

Then z is ...

z = -4(-4) -4(-5) -34 = 16 +20 -34 = 2

The solution is (x, y, z) = (-4, -5, 2).

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You can read more about the cross multiplication method here.

https://brainly.com/question/26397343

Sagot :

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