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==Comparison to linear systems== Systems of nonlinear equations are solved using the same methods we used to solve linear systems, elimin..."

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==Comparison to linear systems==

Systems of nonlinear equations are solved using the same methods we used to solve linear systems, elimination and substitution.

==Solving by substitution (example)==

Solve the following system of equations: <math>3x - y = -2 \text{ and } 2x^2 - y = 0</math>

Solution:

Using the first equation, we see that y = 3x + 2. Substituting 3x + 2 for y in the second equation we see that <math> 2x^2 - (3x + 2) = 0</math>
Now we can solve for x, by using the quadratic formula, or factoring. We find that <math> (2x + 1)(x - 2) = 0</math> or that <math> x = \frac{-1}{2}, 2</math>

Solving back for y, we find that the two points on both curves are <math>(\frac{-1}{2}, \frac{1}{2}), \text{ and }(2, 8)</math>

==Solving by elimination(example)==

Solve the following system by elimination: <math>x^2 + y^2 = 13 \text{ and }x^2 - y = 7</math>

Solution:

We can subtract the second equation form the first to get <math> y^2 + y = 6</math>. We can solve this equation for y to find that y = 2 or -3. For each value of y, we have
2 values for x. So we have four points of intersection <math>(\pm 3, 2), (\pm 2, -3)</math>

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Systems of Nonlinear Equations - Revision history

MathAdmin: Created page with "__TOC__ ==Comparison to linear systems== Systems of nonlinear equations are solved using the same methods we used to solve linear systems, elimin..."

MathAdmin: Created page with "
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==Comparison to linear systems== Systems of nonlinear equations are solved using the same methods we used to solve linear systems, elimin..."