options: 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 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.

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).

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

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
problem_activity: For the following system, determine the values of
$${p, q,}$$
and
$$r$$
that satisfy all three equations:
$$2p + q - r =8$$
$$q + r = 4$$
$${p- q =2}$$


correct_option_index: 4