standard_description: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
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: no