Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.
x² - y = 0
x + y = 2

검증된 단계별 안내

Start with the given system of equations: \[x^2 - y = 0\] \[x + y = 2\]

From the first equation, express \(y\) in terms of \(x\): \[y = x^2\]

Substitute this expression for \(y\) into the second equation: \[x + x^2 = 2\]

Rewrite the equation to standard quadratic form: \[x^2 + x - 2 = 0\]

Solve the quadratic equation using the quadratic formula or factoring to find the values of \(x\), then substitute back to find corresponding \(y\) values using \(y = x^2\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Nonlinear Systems of Equations

A nonlinear system involves equations where variables are raised to powers other than one or multiplied together. Solving such systems requires methods beyond simple substitution or elimination used for linear systems, often involving substitution, factoring, or using the quadratic formula.

Substitution Method

The substitution method involves solving one equation for one variable and substituting that expression into the other equation. This reduces the system to a single equation with one variable, making it easier to solve, especially useful when one equation is already solved for a variable.

Complex Solutions

When solving nonlinear systems, solutions may include complex numbers if the equations lead to negative values under square roots or other operations. Understanding complex numbers and how to express solutions in terms of real and imaginary parts is essential for providing all possible solutions.

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. x2 - y = 0 x + y = 2