options: 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.

Represent a system of linear equations as a single matrix equation in a vector variable.

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
problem_activity: Task
The product of two positive numbers is 9. The reciprocal of one of
these numbers is 4 times the reciprocal of the other number. What is
the sum of the two numbers?


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