If x^2 + y^2 = 29 and x+ y = 7 Then find x and y.
- print Print
- list Cite
Expert Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given the equations:
x^2 + y^2 = 29..............(1)
x+ y = 7.......................(2)
We have a system of two equations and two variables. Then, we can use the substitution or the elimination method to solve.
Let us use the substitution method to solve.
We will re-write equation (2).
x+ y = 7
==> y = 7 - x
Now we will substitute in (1).
x^2 + y^2 = 29
==> x^2 + ( 7-x)^2 = 29
==> x^2 + 49 - 14x + x^2 = 29
==> 2x^2 - 14x + 49 - 29 = 0
==> 2x^2 - 14x + 20 = 0
Now we will divide by 2:
==> x^2 - 7x + 10 = 0
==> ( x - 2) ( x- 5) = 0
==> x1 = 2 ==> y1= 7-2 = 5
==> x2= 5 ==> y2= 7-5 = 2
Then the answer is the pairs:
( 2, 5) OR ( 5, 2)
Related Questions
- If (x^2 - y^2) = 10 and (x + y) = 2, find x and y.
- 2 Educator Answers
- If x^2 - y^2 = 10 and x + y = 5, then x - y = ?
- 1 Educator Answer
- Find x and yIf x^2 + y^2 = 29 and x+ y = 7 Then find x and y.
- 1 Educator Answer
- If x^2-y^2 = 55 and x-y=11, then what is y?
- 1 Educator Answer
- if x+y +z =1 X^2+Y^2+Z^2=2 X^3+Y^3+Z^3=3 then find x^4 +y^4 +z^4=?use algebra
- 1 Educator Answer
This is a symmetric system and we'll solve it using the sum and the product.
We'll note x + y = S and x*y = P
x^2 + y^2 = (x+y)^2 -2xy
x^2 + y^2 = S^2 - 2P
We'll re-write the system in S and P:
S^2 - 2P = 29 (1)
S = 7 (2)
We'll substitute (2) in (1):
49 - 2P = 29
We'll subtract 49 both sides:
-2P = 29 - 49
-2P = -20
We'll divide by -2:
P = 10
We'll substitute P in (1):
S^2 - 20 = 29
We'll add 29 both sides:
S^2 = 49
S1 = 7
S2 = -7
We'll compute x and y:
For S1 = 7 and P = 10
x + y = 7
xy = 10
We'll write the quadratic when we know the sum and the product:
x^2 - 7x + 10 = 0
x1 = [7 + sqrt(49-40)]/2
x1 = (7+3)/2
x1 = 5
x2 = [7 - sqrt(49-40)]/2
x2 = (7-3)/2
x2 = 2
The solutions of the symmetric system are: {(5 ; 2) ; (2 ; 5)}.
If x^2 + y^2 = 29 and x+ y = 7. To find x and y.
(x+y)^2 = x^2+y^2 = 2xy .
Therefore 2xy = (x+y)^2-(x^2+y^2) .
2xy = 7^2-29 = 49-29 = 20.
(x-y)^2 = (x+y)^2-4xy
(x-y)^2 = 7^2-2(20) = 49-40 = 9.
Therefore x-y = sqrt9 = 3.
Thus we have x+y = 7....(1)
x-y = 3....(2).
(1)+(2) gives: 2x= 7+3 = 10. So x= 10/2 = 5.
(1)-(2) gives: 7-3 = 4. So 2y = 4. Or y = 4/2 = 2.
Therefore x= 5 and y = 2.
Student Answers