Solve the system

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Solve the first equation for x: x = y + 2.

Substitute x = y + 2 into the second equation: y^2 = 4(y + 2) + 4.

Simplify the equation: y^2 = 4y + 8 + 4.

Rearrange the equation to form a quadratic equation: y^2 - 4y - 12 = 0.

Solve the quadratic equation for y using the quadratic formula or factoring.

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Concetti chiave

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Systems of Equations

A system of equations consists of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously. Solving such systems often involves substitution or elimination methods to find common solutions.

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Introduction to Systems of Linear Equations

Substitution Method

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

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Choosing a Method to Solve Quadratics

Quadratic Equations

A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. Solutions can be found using factoring, completing the square, or the quadratic formula. Quadratic equations can have two, one, or no real solutions.

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