Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y=?3x and the circle x^2+y^2=3.

Exercises from Illustrative Mathematics A set of 3 exercises, commentary, and solutions

Students solve systems of linear equations in two variables and systems of a linear and a quadratic equation in two variables. Students understand that the points at which the two graphs of the equations intersect correspond to the solutions of the system.

Students develop facility with graphical interpretations of systems of equations and the meaning of their solutions on those graphs. For example, they can use the distance formula to find the distance between the centers of two circles and thereby determine whether the circles intersect in 0, 1, or 2 points. By completing the squares, students can convert the equation of a circle in general form to the center-radius form and, thus, find the radius and center. They can also convert the center-radius form to the general form by removing parentheses and combining like terms. Students understand how to solve and graph a system consisting of two quadratic equations in two variables.