Solving a System of Quadratic and Linear Equations by Substitution

This video tutorial teaches how to solve a system of a quadratic and linear equation using substitution. It begins with an introduction to systems of equations and the substitution method. The tutorial then provides a detailed walkthrough of solving the system, finding solutions, and interpreting these solutions on a graph. Key points include understanding the importance of finding both x and y values and recognizing common mistakes in the substitution process.

What is a system of equations?

• A set of unrelated equations

• An equation with no solution

• A group of equations with a common solution

• A single equation with multiple variables

In the substitution method, what do you replace in one equation?

• The X value with a constant

• The Y value with another expression

• The coefficients with variables

• The entire equation with a new one

What is the first step in solving a quadratic equation using substitution?

• Multiply both sides by a variable

• Add a constant to both sides

• Set the equation equal to zero

• Divide both sides by a coefficient

Which method can be used to solve the quadratic equation after substitution?

• Graphing

• Matrix operations

• Completing the square

• Using logarithms

What do the solutions of the system represent on a graph?

• The axis of symmetry of the parabola

• The points where the line and parabola intersect

• The maximum point of the parabola

• The slope of the linear equation