5 Questions
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 $x^2 - 7x + 6 = 0$?
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 $x=6$.
How do you find the 'y' values that correspond to the solutions of the system of equations?
Use the linear equation to calculate matching 'y' values.
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.
Test your understanding of systems of linear and quadratic equations with this quiz. Solve example equations and learn how to find the intersection points.
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