system_3_eq_2[2] -= system_3_eq_1[2];
    } else if (system_3_eq_1[1] == 0.0 && system_3_eq_2[0] == 0.0) {
        document.getElementById('step_name').innerHTML = "Divided the equations by the respecting coefficients.";
        system_3_eq_1[2] /= system_3_eq_1[0];
        system_3_eq_1[0] = 1.0;
        system_3_eq_2[2] /= system_3_eq_2[1];
        system_3_eq_2[1] = 1.0;
    }
    update_system("system_3");        
    draw_plot_named("system_3");
}

//////
/// quests
function done_system_1_quest_1() {
 