If x and y are positive integers is x - y always positive explain

Mathematics

2 answers:

ozzi3 years ago

6 0

Answer:

No, if y happens to be a larger integer than x, then the result will be negative.

Step-by-step explanation:

For example, lets say that x=4 and y=9, so x-y = 4-9 = -5.

But if we were to reverse it and make x=9 and y=4, then x-y = 9-4 = 5.

r-ruslan [8.4K]3 years ago

3 0

Note that x and y are nonzero integers. It means that x and y will always have same sign (both are either positive or negative, since they are nonzero). Hence, xy term is always positive.

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3 years ago

4x + 3y - z = -6<br> 6x - y + 3z = 12<br> 8x + 2y + 4z = 6

Ket [755]

Answer:

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

Step-by-step explanation:

Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:

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

Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.

Using the first equation to write an expression for z, we have ...

z = 4x +3y +6

Substituting that into the second and third equations gives ...

6x -y +3(4x +3y +6) = 12 ⇒ 18x +8y = -6

8x +2y +4(4x +3y +6) = 6 ⇒ 24x +14y = -18

Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:

3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)

10y = -30

y = -3

Substituting into the first equation (of the equations in x and y), we have ...

18x +8(-3) = -6

18x = 18

x = 1

Finally, substituting into the equation for z gives ...

z = 4(1) +3(-3) +6 = 1

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

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The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.