SOLUTION: Hi Please help me find this (the answers for both X& Y should be integer), the answers are 9& 3 but I don't know the procedure to find them. I really need this to learn so plea

Hi, there--

THE PROBLEM:
Solve for x and y.
X + Y + 6XY = 174

A SOLUTION:
First of all, you are correct that one solution to this equation is (X,Y)=(3,9). There infinitely 
many pairs of X and Y that make this equation true.

One strategy to find solutions would be to rewrite the equation in "Y=" form so you have an 
explicit expression for Y in terms of X.

Isolate the terms that have a Y in them on the left side of the equation by subtracting X from 
both sides.



Factor Y out of each term on the left side.


Divide both sides of the equation by (1-6X).



Once you have the equation in this "Y=" form, you can: 
1. use a graphing calculator to investigate.
2. find any X-intecept by setting the numerator equal to zero.
3. find any y-intercept by setting X=0.

Here is a link to a graph of your equation. Any point on the curve is a solution to the equation.
(You will need to copy and paste it into your browser.

http://graphsketch.com/?eqn1_color=1&eqn1_eqn=(174-X)%2F(1%2B6X)&eqn2_color=2&eqn2_eqn=&eqn3_color=3&eqn3_eqn=&eqn4_color=4&eqn4_eqn=&eqn5_color=5&eqn5_eqn=&eqn6_color=6&eqn6_eqn=&x_min=-17&x_max=17&y_min=-10.5&y_max=10.5&x_tick=1&y_tick=1&x_label_freq=5&y_label_freq=5&do_grid=0&do_grid=1&bold_labeled_lines=0&bold_labeled_lines=1&line_width=4&image_w=850&image_h=525


Hope this helps! Feel free to email if you have any questions.

Mrs. Figgy
math.in.the.vortex@gmail.com