All categories

3 years ago

Solve the system. find x,y, and z please show all steps x-y+z=1 x+y+3z=-3 2x-y+2z=0

Mathematics

1 answer:

Mariulka [41]3 years ago

7 0

Solving the system we get, x= -1, y= -2 and z= 0

Step-by-step explanation:

Solving the equations to find x, y and z

$x-y+z=1\,\,\,eq(1)\\x+y+3z=-3\,\,\,eq(2)\\2x-y+2z=0\,\,\,eq(3)$

Adding eq(1) and eq(2)

$x-y+z=1\\x+y+3z=-3\\--------\\2x+4z=-2\,\,\,\,eq(4)\\$

Adding eq(2) and eq(3)

$x+y+3z=-3\\2x-y+2z=0\\----------\\3x+5z=-3\,\,\,eq(5)$

Multiplying eq(4) by 3 and eq(5) by 2

$6x+12z=-6\\6x+10z=-6\\-\,\,\,-\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\\----------\\2z=0\\z=0$

So, value of z =0

Putting value of z in eq(4)

$2x+4z=-2\\2x+4(0)=-2\\2x=-2\\x=-1$

So, value of x = -1

Now putting value of z=0 and x =-1 in equation 1

$x-y+z=1\\-1-y+0=1\\-y=1+1\\-y=2\\y=-2$

So, value of y = -2

So, solving the system we get, x= -1, y= -2 and z= 0

Keywords: Solve the system

Learn more about Solve the system at:

#learnwithBrainly

You might be interested in

47 is what percent of 188?

katrin [286]

The answer is 47 is 25% of 188.

8 0

3 years ago

Read 2 more answers

Kyleigh put a large rectangular sticker on her notebook. The height of the sticker measures 12 centimeters. The base is half as

saul85 [17]

Height = 12 cm
Base/width —> half of height —> 12/2 = 6 cm

Area = length x width
Area —> 12x6 = 72

The sticker covers 72 cm of the notebook.

8 0

3 years ago

Help, I'm doing rhis problem and need help checking if I'm right.

umka2103 [35]

To me it looks like your right

7 0

3 years ago

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2^x. She makes these

GalinKa [24]

General Idea:

Domain is the values of x which gives a defined output to the function, and Range is the values of y that we get by substituting domain values of x. For the function f(x) = a^x, where a > 0, the domain will be all real numbers and range will be all values greater than 0. That is the graph will be very close to x-axis but will never touch it.

Applying the concept:

From the attached table, we can notice that as x increases infinitely, the y-values are continually doubled for each single increase in x and as x decreases infinitely, the y-values are continually halved for each single decrease in x.

Option 1: "Statement 1 is incorrect because the y-values are increased by 2, not doubled".

Option 1 is INCORRECT because Statement 1 is TRUE & CORRECT.

Option 2: "Statement 2 is incorrect because the y-values are doubled, not halved".

Option 2 is INCORRECT because Statement 2 is TRUE & CORRECT.

Option 3: "The conclusion is incorrect because the range is limited to the set of the integers"

Option 3 is INCORRECT because, the range will be always greater than 0, because irrespective of how many times y is halved for each single decrease in x, the y will still be a positive fraction and won't be a negative.

Option 4: "The conclusion is incorrect because the range is limited to the set of positive real numbers"

Option 4 is CORRECT because y value will be positive irrespective of whatever x we substitute in the function.

8 0

3 years ago

Read 2 more answers

(a) The parametric equations x = f(t) and y = g(t) give the coordinates of a point (x, y) = (f(t), g(t)) for appropriate values

Gnesinka [82]

Answer:

Step-by-step explanation:

a). Given a parametric equation, we are describing a set of coordinates based on the value of t. The variable t is called the parameter.

b) we have the following equations. x=t y=t^2, so in order for us to know where the object is at t=t' we must replace t with the specific value t'. Hence, when t=0 the object is at (0,0^2) = (0,0) (the origin). When t=6, the object is at (6,6^2) = (6,36).

c). To eliminate the parameter, we replace the parameter in one equation by using the second equation. Recall that we have that x=t. Then, by replacing in the second equation, we have the following

$y=t^2 = (x)^2 = x^2$

where $x\geq 0$

5 0

3 years ago