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
MAVERICK [17]
3 years ago
9

What is the solution to the system? 1. x-y + 2 z = -7 2. y + z =1 3. x-2 y - 3 z = 0

Mathematics
1 answer:
kvv77 [185]3 years ago
3 0

You'd find this problem easier to understand and do if you'd please list the defining equations vertically and line up variables:

1. x - 1y + 2 z = -7

2. y + 1z = 1

3. x - 2 y - 3 z = 0 Now eliminate the line numbers:

x - 1y + 2 z = -7

1y + 1 z = 1

x - 2 y - 3 z = 0

Let's use the elimination method to eliminate variable z: Seeing that z = 1 - y, we transform the first equation into 1x - 1y + 2(1-y) = -7

and the third into x - 2y - 3(1-y) = 0.

Simplifying 1x - 1y + 2(1-y) = -7

and x - 2y - 3(1-y) = 0,

we get

1x - 2y - 3 + 3y) = 0 and 1x - 1y + 2 - 2y = -7

which in turn simplify to

1x + y = 3 and 1x - 3y = -9

Having eliminated the variable z, we now focus on eliminating x. Mult. the 1st equation by -1, obtaining -1x - 1y = -3. Add this result to 1x - 3y = -9:

0 - 4y = -12, which tells us that y = 3. Subbing 3 for y in 1x + 1y = 3 tells us that x = 0.

All we have left to determine is the vaue of z.

Borrowing Equation 3, from above, we get x - 2 y - 3 z = 0, and into this equation we substitute x = 0 and y = 3: 0 -2(3) - 3z = 0.

Thus, -3z = 6, and z = -2.

The solution set is (0, 3, -2). You should check this by substitution.

You might be interested in
Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π?
yKpoI14uk [10]
Recall that to get the x-intercepts, we set the f(x) = y = 0, thus

\bf \stackrel{f(x)}{0}=-4cos\left(x-\frac{\pi }{2}  \right)\implies 0=cos\left(x-\frac{\pi }{2}  \right)
\\\\\\
cos^{-1}(0)=cos^{-1}\left[ cos\left(x-\frac{\pi }{2}  \right) \right]\implies cos^{-1}(0)=x-\cfrac{\pi }{2}
\\\\\\
x-\cfrac{\pi }{2}=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}

\bf -------------------------------\\\\
x-\cfrac{\pi }{2}=\cfrac{\pi }{2}\implies x=\cfrac{\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{2\pi }{2}\implies \boxed{x=\pi }\\\\
-------------------------------\\\\
x-\cfrac{\pi }{2}=\cfrac{3\pi }{2}\implies x=\cfrac{3\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{4\pi }{2}\implies \boxed{x=2\pi }
3 0
3 years ago
If f(x)=x^2+1 and g(x)=3x+1 find 2*f(4)
nadya68 [22]
F(x) = x^2 + 1
f(4) = 4^2 + 1 = 16 + 1 = 17
2*f(4) = 2 * 16 = 32
8 0
3 years ago
ASAP help me please thanks
Marianna [84]

Answer: I think it's D

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Change 2/7% to a ratio
andre [41]
(2/7)% = 

<span>(2 / 7) / 100 = </span>

<span>2 / 700 </span>

<span>2 : 698 </span>

<span>1 : 349</span>
7 0
3 years ago
How do i solve this??
avanturin [10]

i do not know the answer

8 0
2 years ago
Other questions:
  • Substitute the ordered pair (5, 3) into the linear equation 2x - 5y = -5 to prove whether it is a solution to the equation.
    14·1 answer
  • Solve the system ⎧⎩⎨⎪⎪⎪⎪⎪⎪4x1−x13x1−3x1−5x2+x2−4x2+3x2+4x3+2x3+6x3+6x3+4x4=+3x4=+7x4=+9x4=3143
    9·1 answer
  • PLEASE HELP!!! I WILL RATE BRAINLIEST TO THE FASTEST AND CORRECT ANSWER!!!
    7·1 answer
  • The walls of a room are representations of what basic element of geometry? A. point B. line C. plane D. ray
    10·2 answers
  • A catering service offers lasagna and chicken Parmesan. Each pan serves 24 people. Right in equation to represent the number of
    10·2 answers
  • Using the distributive property how can I rewrite the expression 4*24
    8·1 answer
  • Jason already knew 5 appetizer recipes before starting culinary school,and he will earn 1 new appetizer recipe during each week
    7·1 answer
  • What point represents 3/4 x 1/2
    7·1 answer
  • What percent is 272 out of 355?
    11·1 answer
  • Help me fro brainleist.........
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!