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Mastering Systems of Linear and Quadratic Equations

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Mastering Systems of Linear and Quadratic Equations

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Questions and Answers

What is the first step in solving a system of linear and quadratic equations?

Make both equations into 'y=' format.

What is the second step in solving a system of linear and quadratic equations?

Set the equations equal to each other.

How do you simplify the equation $x^2 - 5x + 7 = 2x + 1$ into the 'standard quadratic equation' format?

Subtract $2x$ from both sides to get $x^2 - 7x + 7 = 1$. Then subtract $1$ from both sides to get $x^2 - 7x + 6 = 0$.

How do you factor the quadratic equation $x^2 - 7x + 6 = 0$?

<p>Rewrite $-7x$ as $-x-6x$ to get $x^2 - x - 6x + 6 = 0$. Then factor out common terms to get $(x-1)(x-6) = 0$. The solutions are $x=1$ and $x=6$.</p> Signup and view all the answers

How do you find the 'y' values that correspond to the solutions of the system of equations?

<p>Use the linear equation to calculate matching 'y' values.</p> Signup and view all the answers

Study Notes

Solving Systems of Linear and Quadratic Equations

The first step in solving a system of linear and quadratic equations is to write one of the equations in the standard form of a linear equation (y = mx + b) or quadratic equation (ax^2 + bx + c = 0).

Simplifying Quadratic Equations

To simplify the equation x^2 - 5x + 7 = 2x + 1 into the standard quadratic equation format, subtract 2x + 1 from both sides of the equation and then combine like terms, resulting in x^2 - 7x + 6 = 0.

Factoring Quadratic Equations

To factor the quadratic equation x^2 - 7x + 6 = 0, look for two numbers whose product is 6 and whose sum is -7, and then rewrite the equation as (x - 1)(x - 6) = 0.

Finding Corresponding 'y' Values

To find the 'y' values that correspond to the solutions of the system of equations, substitute the solutions (x-values) back into one of the original equations, and then solve for y.

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Description

Test your understanding of systems of linear and quadratic equations with this quiz. Solve example equations and learn how to find the intersection points.