1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nikklg [1K]
3 years ago
12

Need help finding the x, y, and z. please and thank you

Mathematics
1 answer:
Reptile [31]3 years ago
4 0

The first step in any problem is to look at what you are given. When solving systems of linear equations, it is often helpful to eliminate one or more of the variables by adding or subtracting a multiple of one equation with a multiple of another. It is convenient when at least one of the multipliers is 1.

Here, we can cancel the y-terms in the 2nd and 3rd equations simply by adding them together. This gives

... (5x +y -4z) +(-3x -y +5z) = (41) +(-45)

... 2x +z = -4 . . . . simplified

Likewise, we can add 3 times the second equation to the first to cancel y in that sum.

... 3(5x +y -4z) +(2x -3y +z) = 3(41) + (-1)

...15x +3y -12z +2x -3y +z = 123 -1

...17x -11z = 122 . . . . simplified

Now that we have 2 equations in x and z, we can go through the same process. We observe that the coefficient of z is +1 in the first equation and -11 in the second. The means we can cancel the z terms by adding 11 times the first equation to the second:

... 11(2x +z) +(17x -11z) = 11(-4) +122

...22x +17x = 78 . . . . . . simplify a little bit

... x = 78/39 = 2 . . . . . . divide by 39

From above, we find

... z = -4 -2x = -4 -2·2 = -8

... y = 41 -5x +4z = 41-5(2) +4(-8) = 41 -42 = -1

The solution is (x, y, z) = (2, -1, -8).

_____

The method of elimination used here will vary with the system of equations. If you want to employ a consistent method, you can use Cramer's Rule, Gaussian elimination, or matrix methods. Since you apparently don't mind help from technology, learning to do this on your graphing calculator can also be a good idea.

You might be interested in
Plz help I need help
Kamila [148]

Answer:

Sub to XxDuckyxX it has 225

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The graph shows a rectangle that has been rotated. Which statement is FALSE?
lukranit [14]
D. Is the false statement. Clearly, the rectangle was shifted and is no long in its same position
7 0
3 years ago
Read 2 more answers
Write an algebraic expression for product of 10 and the sum of x and 8
egoroff_w [7]
That would be the same as : 10 × (x + 8)

Okay, so it's asking for the product of 10, and the sum of 8 and k. Sum is the answer to an addition problem, so that would make the last of it 8 + k. And we'd be multiplying this with 10, so that would make it : 10 × (x + 8)
5 0
3 years ago
ABCd is a parallel. Which statements are true
Leviafan [203]
Confused on the question could I have a picture?
8 0
3 years ago
What is the factored form of the polynomial? X^2 -12+27?
Natali5045456 [20]

Answer:

(x-9)(x-3)

Step-by-step explanation:

Look to the number on the right, 27, and list out the factors. (1 and 27, 3 and 9, -1 and -27, -3 and -9)

Next, find the factors that would equal the middle number, -12, when added. -3 and -9 add to -12. Therefore, choose these numbers and put them in the form (x-9)(x-3).

5 0
3 years ago
Other questions:
  • Helpppppppppppppppppppppppppppppp
    8·1 answer
  • Just the answer please
    13·2 answers
  • Write an equation to represent m varies inversely as the square of q ?​
    6·1 answer
  • Does anyone know the answer to this question? −9y>9
    15·2 answers
  • Andy has a watering can that contains 20 cups of water, he pours one quart of water on each plant in his yard if he uses all the
    12·1 answer
  • Find the solution to the system. Write your solution as an ordered pair (x,y) with no spaces, no solution, or infinitely many. y
    13·2 answers
  • PLEASE HELP !! ILL GIVE BRAINLIEST !!
    11·2 answers
  • i need help with this one Eight cookies cost $12. At this rate, how much will 10 cookies cost? soory i didnt see the answer
    8·1 answer
  • A new law has support from some Democrats and some Republicans. This two-way frequency table shows the proportion from each poli
    11·1 answer
  • What is the domain of the function y=3 In x graphed below?​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!