# Math Help - Systems of nonlinear equations in two variables

1. ## Systems of nonlinear equations in two variables

Can you please check my answers?

Solve the system by the substitution method.

-12x-y=22
y=x^2+10

answer: {(-8,74), (-4,260)}

x+y=8
y=x^2-4x+4

answer: {(4,4), (-1,9)}

y=x-4
y^2=-16x

answer: {(-4,-8)}

x^2+y^2=41
x+y=9

answer: {(5,4),(4,5)}

Solve the system by the substitution method.

x^2+y^2=36
x^2-y^2=36

answer: {(6,0), (-6,0)}

7x^2+y^2=49
7x^2-y^2=49

answer:{(square root 7,0), (negative square root 7,0)}

x^2+y^2=4
4x^2+9y^2=36

answer: {(0,2),(0,-2)}

x^2-y^2=25
4x^2+25^2=100

answer: {(5,0), (-5,0)}

2. Originally Posted by soly_sol
Can you please check my answers?

Solve the system by the substitution method.

-12x-y=22
y=x^2+10

answer: {(-8,74), (-4,260)}
I assume this is a typo: the second pair is (-4, 26).

Originally Posted by soly_sol
x+y=8
y=x^2-4x+4

answer: {(4,4), (-1,9)}

y=x-4
y^2=-16x

answer: {(-4,-8)}

x^2+y^2=41
x+y=9

answer: {(5,4),(4,5)}

Solve the system by the substitution method.

x^2+y^2=36
x^2-y^2=36

answer: {(6,0), (-6,0)}

7x^2+y^2=49
7x^2-y^2=49

answer:{(square root 7,0), (negative square root 7,0)}

x^2+y^2=4
4x^2+9y^2=36

answer: {(0,2),(0,-2)}

x^2-y^2=25
4x^2+25^2=100

answer: {(5,0), (-5,0)}
These are all good. (In the last problem, I presume the second equation is really $4x^2 + 25y^2 = 100$.

-Dan