SOLUTION: Hello, I'm stumped on yet another problem... Solve the following nonlinear system by substitution: {{{ x^2+y^2=10 }}} {{{ -3x+y=0 }}} In advance, THANKS SO MUC

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In the first equation both of the variables are squared and in the second equation both of the variables are to the first power. In other words, there is no way that we can use elimination here and so we are must use substitution


solve the second equation for y and substitute this into the first equation.
y = 3x
x^2 +(3x)^2 =10
x^2 +9x^2 =10
10x^2 =10
x^2 = 10/10=1
x^2=1
x= (sqrt(1))=+/- 1
So, we have two values of x. Now, we need to determine the values of y
We determine the values of y by plugging x into our substitution.
y=3x
y=3(-1)=-3
y=3(1) =3

Now, we only have two solutions here
We get y=3 as a solution ONLY if x= 1 and so the first solution is,
x = 1 , y=3
Likewise, we only get y=-3 ONLY if x = -1 and so the second solution is,
x=-1 ,y=- 3