What is the solution set to the following system? {x+y=3 {x^2+y^2=9
1 answer:
There are two solutions
The first solution is (x,y) = (3,0)
The second solution is (x,y) = (0,3)
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Work Shown:
Isolate x in the first equation (subtract y from both sides)
x+y = 3
x = -y+3
Now plug this into the second equation. Isolate y.
x^2 + y^2 = 9
(-y+3)^2 + y^2 = 9 ... replace x with -y+3
y^2 - 6y + 9 + y^2 = 9 ... FOIL rule
2y^2 - 6y + 9 = 9
2y^2 - 6y = 0
2y(y-3) = 0
2y = 0 or y-3 = 0 .... zero product property
y = 0 or y = 3
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If y = 0, then x is
x = -y+3
x = -0+3
x = 3
Therefore, x = 3 and y = 0 pair up to get the ordered pair (x,y) = (3,0) as one solution of this system
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If y = 3, then x is
x = -y+3
x = -3+3
x = 0
Therefore, x = 0 and y = 3 pair up to get the ordered pair (x,y) = (0,3) as the other solution of this system
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If you were to graph the two equations, you should find that the curves cross each other at (0,3) and (3,0). I've marked these two points as A and B respectively. The order of the solutions does not matter.
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<h2>Explanation:</h2><h2></h2>
Hello! Remember you have to write complete questions in order to get good and exact answers. Here you forgot to write the relation so I could help you providing my own relation.
Remember that for any relation, we have a set that matches the the domain (also called the set of inputs) of the function and the set
that contains the range (also called the set of outputs).
Suppose our relation is:
So the x-values represents the set A and the y-values the set B. Therefore, by evaluating the x-values into our relation we get:
So in this context, the correct option is:
B) (-9,-8, -7, -6, -5}