how to solve simultaneous equation x-y=5 , x^2+2xy+y^2=9?

Question

pls show step by step to me.. coz i'm confuse to dis ques.. tqtq

Answer 1

(x-y=5
(x²+2xy+y²=9

Equation I: x = 5+y
Equation II: x²+2xy+y²=9
Substitution: (5+y)² + 2(5+y)y+y²=9
25+2.5.y + y² +10y + 2y² + y² = 9
4y² + 20y + 25 - 9 = 0
4y² + 20y + 16 = 0 (:4)
y² + 5y + 4 = 0
d = 5² - 4.1.4
d = 25 - 16 = 9
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y = (-5 +/-\/9) : 2
y' = (-5 + 3):2
y' = -2:2 = -1
y" = (-5-3):2
y" = -8:2 = -4
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x = 5+y
For y = -1; x' = 5-1 = 4
For y = -4; x"= 5 -4 = 1
\/ = root
Solution: {x, y elements of R| x= 4 and x = 1; y' = -1 and y" = -4}
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Answer 2

Step 1: Simplify x^2+2xy+y^2 as (x+y)^2.
Step 2: (x+y)^2=9
Step 3: So (x+y)= square root of 9

If we solve the above eqn there are 2 solutions..
1.x+y=+3
2.x+y=-3 as square root of x^2 is+x,-x.
Step 4: we have (x-y=5) &(x+y=+3)
adding these two we get x-y+x+y=5+3
2x=8 so x=4.
substitute for x=4 in x-y=5 we have y=x-5=4-5= -1

Step 5: we also infer that (x-y=5) & (x+y=-3)
adding these two we get x-y+x+y=5-3
2x=2 so x=1
substitute for x=1 in x-y=5 we have y=x-5=1-5= -4

Step 6 so we have values x=4,1
y=-1,-4

Answer 3

xy+x+y=5 provides x( a million+y)= 5-y x= 5-y / (a million+y) 2xy+x+3y=9 2 y * (5-y) / (a million+y)+ (5-y) / (a million+y)+3 y =9 set up you will get 2 y (5-y) + (5-y) +3y (a million+y) = 9 (a million+y) y^2 +3y -4 =0 provides y = a million and y = -4 for y = a million ; x = 2 for y=-4 ; x = -3

Answer 4

Add y from both sides:
x=y+5

Just substitute it in the second equation:
(y+5)^2+2y(y+5)+y^2=9
y^2+10y+25+2y^2+10y+y^2=9
4y^2+20y+25=9
4y^2+20y+16=0
(2y+2)(2y+8)=0
y=-1 and -4

x+1=5
x=4

x+4=5
x=1
x=4 and 1

Check:
4-(-1)=5
4+1=5
5=5

1-(-4)=5
1+4=5
5=5

(4)^2+2(4*-1)+(-1)^2=9
16-8+1=9
8+1=9
9=9

(1)^2+2(1*-4)+(-4)^2=9
1-8+16=9
-7+16=9
9=9

The solution sets are (4,-1) and
(1,-4)

Answer 5

1) Use Intercept metho
like this
x-(0)=5
x=5
0-y=5
y=-5
then the points are (5,-5)
...do the same on both equations
2) plot the two unknowns on a Cartesian plane
3) If they intersect, the intersection point will satisfy the equation, this is called inconsistent. If they dont intersect they dont have the same eq. this means the are parrallel it is called inconsistent, the two equations have no same answer. If they are on top of each other they have many solutions then, the solution can be any of the point on it, this is called dependent

Now try it on your equation
Hope I helped you

Answer 6

x-y=5
so x=y+5
sub in second equation
(y+5)^2+2y(y+5)+y^2=9
y^2+10y+25+2y^2+10y+y^2=9
4y^2+20y+16=0
divide the whole eq by 4
y^2+5y+4=0
(y+4 )(y+1 )=0
so y =-4 x=+1
or y=-1 x=+4

Answer 7

x-y=5
x^2+2xy+y^2=9

x - y = 5
(x+y)^2 = 9

x - y = 5
x + y = 3
or
x - y =5
x + y =-3

x = 4 y = -1 or x = 1 y = -4

Answer 8

1) We have, x-y=5
2) Remember the formula, (x+y)^2 = x^2 + 2xy + y^2
3) So, we have (x+y)^2 = 9
4) So, x+y = 3 or x+y = -3

Case I (x+y=3)
Then, adding both eqns

x - y = 5
+ x + y = 3
---------------
2x = 8

So, x = 4
4+ y = 3
y = 3-4
y = -1
So, x=4, y= -1

Case 2 (x+y = -3)
Adding both eqns

x - y = 5
+ x + y = -3
----------------
2x = 2
x = 1
1 + y = -3
y = -3-1
y = 4
So, x = 1, y = -4

So, we have two solns
1) x = 4, y = -1
2) x = 1, y = -4

Both, these solns satisfy your given eqns

Answer 9

x-y=5 and x*x+y*y+2*x*y=9
that is (x+y)*(x+y)=9
that is x+y=3 (as 3*3=9) and x+y=-3 (as -3*(-3)=9).
on solving x-y=5 and x+y=3 we get x=4,y=-1.
On solving x-y=5 and x+y=-3 we get x=1 and y =-4.

Answer 10

x-y=5,
Thus,
x=5+y

Sub this into x^2+2xy+y^2=9
you get (5+y)(5+y)+2(5+y)(y)+(y)(y)=9

solve for the value of y, then sub value of y into x=5+y, you will get x.