SOLUTION: How do you solve a system of equations with two equations that are non linear if you have both of the following?
{{{ x = 3-y }}}
{{{ y = sqrt(x+3) }}}
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-> SOLUTION: How do you solve a system of equations with two equations that are non linear if you have both of the following?
{{{ x = 3-y }}}
{{{ y = sqrt(x+3) }}}
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Question 1103940: How do you solve a system of equations with two equations that are non linear if you have both of the following? Found 2 solutions by ikleyn, josgarithmetic:Answer by ikleyn(52831) (Show Source):
You can put this solution on YOUR website! .
How do you solve a system of equations with two equations that are non linear if you have both of the following?
~~~~~~~~~~~~~~~~~~~~~~
x = 3-y, (1)
y = . (2)
In problems like this, the square root in equation (2) is the POSITIVE branch of the square root, so it is POSITIVE.
Square the equation (2) (both sides). You will get
y^2 = x + 3.
Now replace "x" in this last equation by 3-y, based on (1). You will get
y^2 = (3-y) + 3, or
y^2 + y - 6 = 0.
= = = .
Now, only positive "y" is acceptable, as I said above.
So, y = = 2 is the only solution.
Then x = 3-2 = 1.
Answer. The solution is x = 1, y = 2.
You can easily check it.
Below is the graph of participating functions.
Plot y = 3-x (red) and y = (green)
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