SOLUTION: Help On This Will Be Great Appreciated<3
Solve The Non-Linear system of Equations. Give Exact Values.
{{{x^2+y^2=10}}}
{{{3y=x^2+8}}}
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Question 170266: Help On This Will Be Great Appreciated<3
Solve The Non-Linear system of Equations. Give Exact Values.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Solve:
Rewrite this as and substitute into the 1st equation.
Simplify.
Factor.
Apply the zero product rule.
or
Use the positive solution and substitute into the second equation to solve for x.
Substitute y = 3.
Subtract 8 from both sides.
Take the square root of both sides.
or
The solution consists of two points of intersection:
(1, 3) and (-1, 3)
-------------------
Just for interest, since we had two solutions for y (y = 3 and y = -6), let's see what happens when we choose the second solution of y = -6 and substitute into the first equation to solve for x.
Substitute y = -6.
Subtract 8 from both sides.
Take the square root of both sides.
or and, as you can see, the results are "imaginary" numbers, so there is no "real" solution for y = -6.
---------------------------
Let's see what the graph of these two functions look like:
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