Question

solve the system of equations using substitution.

x^2 + y^2 = 61
x + y = 11

Answer 1

Solve for one of the variables in x+y=11

Answer 2

Then plug that in for one of the variables in the other equation

Answer 3

i have to use substitution. so i have to plug one of them into the other.

Answer 4

...that's what I said :3 That's what substitution is. Say you want to find x first. Solve for y in x+y=11, which would be y=11-x, and substitute that for y, then solve for x.

Answer 5

You would get x^2+(11-x)^2=61

Answer 6

Solve that for x, then use x and solve for y in the same equation.

Answer 7

Well, do it. y = 11 - x

\(x^{2} + (11-x)^{2} = 61\)

That's about as simple as any other Quadratic Equation. Let's see what you get.

Keep in mind a circle and a line can produce three possible results:
1) No intersection at all.
2) One tangent intersection.
3) Two intersections.

Answer 8

ok wait :)

Answer 9

yeah well i know its going to be two intersections :)

Answer 10

Fair enough, but they are a little funny and the casual observer may think there is only one.

Answer 11

no, the solutions are (6,5) (5,6)

Answer 12

Good call. Their reflection on x = y can be confusing. I am glad to see you were not confused.

Answer 13

x^2 + y^2 = 61
x + y = 11
------------
By substitution.

x + y = 11
y = 11 - x

Answer 14

Substituting (11 - x) for y in --> x^2 + y^2 = 61

Answer 15

x^2 + (11 - x) ^2 = 61

x^2 + 121 -22x + x^2 = 61

Answer 16

okaii got all that until now:)

Answer 17

2 x^2 - 22x + 121 = 61

2x^2 -22x + 60 = 0

Answer 18

x^2 - 11x + 30 = 0

(x - 6) ( x - 5) = 0

x - 6 = 0 OR x - 5 = 0

x = 6 OR x = 5

Answer 19

x = 6 OR x = 5
--------------

Let x = 6.

Then, y = 11 - x
y = 11 - 6
y = 5

One set of coordinates for one point of intersection is (6,5) -->

Answer 20

Let x = 5
---------

y = 11 - x
y = 11 - 5 = 6.

The second set of coordinates for the second point of intersection is (5, 6) -->

Answer 21

thanx man :)))))

Answer 22

Glad to help.