Mathematics, 19.08.2020 18:01 ellllaaaxx

Solve 3x+2y−z=2 2y+z=7 −2x−4z=−2 Enter your answer, in the form (x, y,z), in the boxes in simplest terms. x= y= z=

Answers: 3

Show answers

Answers

Answer from: ashleygervelus

(-1, 3, 1)

x=-1, y=3, z=1.

Step-by-step explanation:

So we have the three equations:

$3x+2y-z=2\\2y+z=7\\-2x-4z=-2$

And we want to find the value of each variable.

To do so, look at the equations and try to think about what we can do to isolate one of the variables by itself.

We can see that both the second and equation has a variable and then the variable z.

In other words, we can solve for y in the second equation and x in the third equation and then substitute them in the first equation to isolate the variable z and then solve for z. With that, we can then easily arrive at our solution.

Therefore, solve for y in the second equation:

2y+z=7

Subtract z from both sides. The zs on the left side cancels:

$(2y+z)-z=(7)-z\\2y=7-z$

Now, divide both sides by 2. The 2s on the left cancel and we've isolated the y variable:

$\frac{(2y)}{2} = \frac{(7-z)}{2}\\y=\frac{(7-z)}{2}$

Now, do the same for the third equation. Isolate the x variable:

-2x-4z=-2

First, divide everything by -2 to make things simpler:

$\frac{(-2x-4z)}{-2}=\frac{(-2)}{-2}\\ x+2z=1$

Now, subtract 2z from both sides to isolate the x variable:

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

We have isolated the x and y variables. They are:

$y=\frac{(7-z)}{2}\\x=1-2z$

Now, we can substitute them back into the first equation. Therefore:

$3x+2y-z=2\\3(1-2z)+2(\frac{7-z}{2})-z=2$

Distribute the first and second terms. The second term cancels out:

$3(1)-3(2z)+(7-z)-z=2\\3-6z+7-z-z=2$

Combine like terms:

$-6z-z-z+3+7=2\\-8z+10=2\\$

Subtract 10 from both sides:

$(-8z+10)-10=2-10\\-8z=-8$

Divide both sides by -8:

z=1

Now that we've determined that z=1, plug it back into the isolated second and third equations:

Second equation:

$y=\frac{(7-z)}{2}\\y=(7-1)/2\\y=(6)/2=3$

Third equation:

$x=1-2z\\x=1-2(1)\\x=1-2=-1$

Therefore, our answer is (-1, 3, 1)

Answer from: viridianasar5158

(x, y, z) = (-1, 3, 1)

Step-by-step explanation:

Any of a number of web sites will solve systems of equations for you. Your graphing calculator will, too.

The solution is the right-most column in reduced row echelon form. Top to bottom, the variables are in order x, y, z.

(x, y, z) = (-1, 3, 1)

_____

If you like, you can use substitution to do this by hand.

z = 3x +2y -2 . . . . from the first equation

2y +(3x +2y -2) = 7 . . . . substituting into the second equation

3x +4y = 9 . . . . . in standard form

-2x -4(3x +2y -2) = -2 . . . . substituting for z into the third equation

14x +8y = 10 . . . . . in standard form

Subtract half the second equation from the first:

(3x +4y) -(7x +4y) = (9) -(5)

-4x = 4 . . . simplify

x = -1 . . . . . divide by 4

y = (9 -3x)/4 = (9 -3(-1))/4 = 12/4 = 3

z = 3(-1) +2(3) -2 = 1

The solution is (x, y, z) = (-1, 3, 1).

Solve 3x+2y−z=2 2y+z=7 −2x−4z=−2 Enter your answer, in the form (x,y,z), in the boxes in simplest te

Answer from: Quest

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

Answer from: Quest

Here for a good time of free question aha

Another question on Mathematics

Mathematics, 21.06.2019 14:00

The jones farm has 24 cows that each produce 52 quarts of milk a day. how many quarts are produced each day altogether

Answers: 1

Answer

Mathematics, 21.06.2019 15:30

Adepartment store purchases screen-printed t-shirts at a cost of $5 per shirt. they mark up the price 150% (making the selling price 250% of the store's purchase price) and put them on the sales floor. every month that a t-shirt doesn't sell, the store reduces the selling price by 25%.

Answers: 3

Answer

Mathematics, 21.06.2019 17:30

One line passes through (-7,-4) and (5,4) . another line passes through the point (-4,6) and (6,-9)

Answers: 1

Answer

Mathematics, 22.06.2019 02:30

Atrain traveled for 1.5 hours to the first station, stopped for 30 minutes, then traveled for 4 hours to the final station where it stopped for 1 hour. the total distance traveled is a function of time. which graph most accurately represents this scenario? a graph is shown with the x-axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the origin and moves upward for 1.5 hours. the line then continues upward at a slow rate until 2 hours. from 2 to 6 hours, the line continues quickly upward. from 6 to 7 hours, it moves downward until it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y axis labeled total distance (in miles). a line is shown beginning at the origin. the line moves upward until 1.5 hours, then is a horizontal line until 2 hours. the line moves quickly upward again until 6 hours, and then is horizontal until 7 hours a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the y-axis where y equals 125. it is horizontal until 1.5 hours, then moves downward until 2 hours where it touches the x-axis. the line moves upward until 6 hours and then moves downward until 7 hours where it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at y equals 125 and is horizontal for 1.5 hours. the line moves downward until 2 hours, then back up until 5.5 hours. the line is horizontal from 5.5 to 7 hours

Answers: 1

Answer

You know the right answer?

Solve 3x+2y−z=2 2y+z=7 −2x−4z=−2 Enter your answer, in the form (x, y,z), in the boxes in simplest t...

Questions

Mathematics, 10.12.2020 02:30

Which of the following is closest to the area of the shaded region below?

Mathematics, 10.12.2020 02:30

a department store sells logo shirts at an original price of $20 each month the t-shirts don't sell the store reduces the price sale by 25% markdown g...