Help with Algebra

Question

I have to express each equation in slope-intercept form. Without graphing the equation, state whether the system of equations has exactly one solution, no solution, or an infinitive number of solutions. 

 

x+y=-4

x-y=17

Answer 1

By adding the two given equations together, you get 2x = 13 so x = 13/2 = 6.5

Then y = -4 - 6.5 = -10.5.

So these two lines intersect at (6.5, -10.5) i.e. there's a single point of solution.

 

Had you put each into slope-intercept form, which I really easy to do (in each equation, "solve for y") you would have observed that the two lines have different slopes and hence they must intersect--exactly one solution.