SOLUTION: x^2 + y^2 = 9 x + y = 2 x = ? or ? y = ? or ? Give answer to 2 decimal places

Question 846641: x^2 + y^2 = 9
x + y = 2
x = ? or ?
y = ? or ?
Give answer to 2 decimal places
Found 2 solutions by Fombitz, josh_jordan:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Intersection of a circle and a straight line.
Substitute,

Use quadratic formula,

Then,

Remember the +/- sign should be -/+ but the symbol doesn't exist here.
(,)
and
(,)
.
.
.

Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
To solve this system of equations, first, rewrite the second equation in terms of either x or y. I will rewrite it in terms of y. So, I will rewrite x + y = 2, as y = 2 - x. Next, replace y in equation 1 with 2 - x:

----->

----->

Next, combine like terms:

Now, subtract 9 from both sides, giving us this equation in quadratic form:

----->

You will notice this equation cannot be factored with integers, so we can use the quadratic equation to find the values of x:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=56 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.87082869338697, -0.870828693386971. Here's your graph:

Rounding to two decimal points gives us x: 2.87 or -0.87

To find y, replace each of these values for x in our second equation x + y = 2:

2.87 + y = 2 ----->

y = 2 - 2.87 ----->

y = -.87

AND

-0.87 + y = 2 ----->

y = 2 + 0.87 ----->

y = 2.87

SO, x = 2.87 or -0.87 and y = 2.87 or -0.87
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