Question

Find the pair of negative integers x and y such that x-y=5 and y-x=-4

Answer 1

Answer:

x-y=5

x=5+y

y-x=-4

putting x value in these equation,we get

y-(5+y)=-4

y(-5-y)=-4

-5y-y^2=-4

y^2+5y+4=0

y^2+4y+y+4=0

y(y+4)+(y+4)=0

(y+4)(y+1)=0

y=-4 or y=-1

so,x=5+y

=5-4=-1

or x=5-1=4

I hope,it will help u.....

Answer 2

Answer:

The are no pair of negative integers which can satisfy both of the equation as the given equation have plots parallel to each other.

Step-by-step explanation:

The two pair of given equations are given as follows:

x - y = 5           ...(i)

y - x = -4          ...(ii)

Here after comparing to the general form of pair of linear equation of two variable, i.e., $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$, we get:

$a_1$ = 1, $b_1$ = 1 and $c_1$ = -5

$a_2$ = 1, $b_2$ = 1 and $c_2$ = 4

Now, we know that for a pair of linear equation of two variables, if the following conditions are satisfied, they do not have any real solution:

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

By applying this condition to the given set of equation, we can see if there is any real existent solution for the set of equations:

$\frac{1}{1}=\frac{1}{1}\ne \frac{-5}{4}$

Thus, no pair of real roots and solutions exist for the given set of pair of linear equations of two variables.

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