To do this in Sage, I tried the following, which worked:

var("x y") solve( [11x+15y+23 ==0, 7x-2y-20 == 0], [x,y] )

However, I'm wondering if what you really want to know is how to do this by hand... If so, please consider reading

• Ch 1, Sec 2 "Intersecting Two Lines, Part One"
• Ch 1, Sec 3 "Intersecting Two Lines, Part Two"

of my free electronic online textbook-in-progress for the freshmen math course that business majors take: "Finite & Financial Mathematics for University Freshmen." All you have to do is:

• Go to www.gregorybard.com
• Click on "Finite Math" on the left hand side of the page
• Each section is its own pdf file.