## Standards with the same topic and subject but for other grades

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.

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.

Explain why the πΉ-coordinates of the points where the graphs of the equations πΊ = π§(πΉ) and πΊ = π(πΉ) intersect are the solutions of the equation π§(πΉ) = π(πΉ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π§(πΉ) and/or π(πΉ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

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

Explain why the πΉ-coordinates of the points where the graphs of the equations πΊ = π§(πΉ) and πΊ = π(πΉ) intersect are the solutions of the equation π§(πΉ) = π(πΉ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π§(πΉ) and/or π(πΉ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.