For every value of a, the graph of each of these three equations is a line:
ax + y = 1
x + ay = 1
x + y = 9
For what value of a do all three of these lines intersect at the same point?
Add the first two equations
ax + y + x + ay = 2 simplify
a ( x + y) + (x + y) = 2 { remember that x + y = 9 }
a (9) + (9) = 2
9a = 2 - 9
9a = -7
a = -7/9
See the graph here : https://www.desmos.com/calculator/1tn3bcfeqk
