If x^2 + y^2 = 29 and x+ y = 7 Then find x and y.

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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 =...

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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)

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