standard_description: 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.
problem_activity: Problem 1
Without solving the systems, explain why the following system must have the same solution.
| System 1:                       $${4x-5y=13 }$$                        $${3x+6y=11}$$ | System 2:                       $${8x-10y=26}$$                        $${x-11y=2}$$ |
|---------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------|
Problem 2
Solve the system of equations by writing a new system that eliminates one of the variables.
$${3x+2y=4}$$
$${4x+7y=1}$$


aligns: yes