Question

What is the solution of 3x + y = 9 and 3x − 5y = 15?

Answer 1

So there are two ways.
First you could solve for y and plug it into the calculator. one equation for y1 and another for y2. Then go 2nd trace and press 5 and then press enter 3 times  to find the intersection. 
the second way is to solve by hand. I would suggest solve the first equation for y and plug the equation solved for y into the other equation. so y = -3x + 9 and 3x-5y=15. Then you could do 3x - 5(-3x+9) = 15. Finally solve for x and plug in x into both equations to see if you get the same y value. 
The answer should be (10/3, -1) 

Answer 2

$\left \{{{3x+y=9} \atop {3x-5y=15}} \right. \\ \left \{ {{y=9-3x} \atop {3x-5(9-3x)=15}} \right. \\ \left \{ {{y=9-3x} \atop {3x-45+15x=15}} \right. \\ \left \{ {{y=9-3x} \atop {18x=60}} \right. \\ \left \{ {{y=9-3x} \atop {x= \frac{60}{18} }} \right. \\ \left \{ {{y=9-3x} \atop {x= \frac{10}{3} }} \right. \\ \left \{ {{y=9-3 \frac{10}{3} } \atop {x= \frac{10}{3} }} \right. \\ \left \{ {{y=-1} \atop {x= \frac{10}{3} }} \right.$