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Method

Solving Nonlinear Systems Using Substitution

In a similar way that a system of linear equations can be solved using the substitution method, there are nonlinear systems that can be solved by substituting. As an example, consider the following linear-quadratic system.
This system is solved using substitution following the steps below.
1
Finding a Term to Substitute
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The first step to solve a nonlinear system using substitution is to identify which term is substituted from one equation to the other. The given system has the variable already isolated so it is easy to select that term.
2
Substituting a Term
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Now the value of from Equation (II) is substituted into Equation (I). Then, the resulting equation is simplified as much as possible.
A quadratic equation that only depends on was obtained.
3
Solving the Resulting Equation
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A quadratic equation was obtained from the previous step. This equation is written in standard form.
These values can be substituted into the quadratic formula.
There are two possible values for depending if there is a subtraction or an addition. These values are calculated individually.
4
Substituting the Values
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To find the values of the values of and are substituted into either equation of the system. It is easier to substitute the values into Equation (II) because it is a linear equation, instead of quadratic.

This indicates that the solutions of the system are the points and

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