Mathematics, 04.08.2019 17:30 222364

What is the solution of the following system? {x+y+z=6, x-y+z=8, x+y-z=0

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Answer from: 120175

Much easier to use elimination method to solve this problem

Given system of equation
x + y + z = 6 (this is first equation)
x - y + z = 8 (this is second equation)
x + y - z = 0 (this is third equation)

FIRST
I'm going to eliminate x and y from the first and third equation to find the value of z
x + y + z = 6
x + y - z = 0
- (substract)
2z = 6
z = 3
The value of z is 3

SECOND
I'm going to x and z from the first and third equations to find the value of y.
x + y + z = 6
x - y + z = 8
- (substract)
2y = -2
y = -1
The value of y is -1

THIRD
I'm going to use subtitution method to find x. I'm subtituting the value of y and z to one of the equation.
x + y + z = 6
x + (-1) + 3 = 6
x + 2 = 6
x = 4
The value of x is 4

The solution is (4,-1,3)
x = 4
y = -1
z = 3

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

step-by-step explanation:

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What is the solution of the following system? {x+y+z=6, x-y+z=8, x+y-z=0...