Question

Please Help!
The system
x-y=-1
2x+y=4 has
a.)no solution
b.)a unique solution
c.)an infinite number of solutions

Answer 1

well you can solve this problem with different methods. I will use substitution. In the first equation we solve for x giving us \[x=y-1\]
then we can substitute this into the second equation in place for x. Since we know what x is in the first equation in terms of y and we have to find the intersection or the "solution" we can substitute in the second equation for x because at the end of the day, for our solution, x and y are the same in both equations.
\[2(y-1)+y=4\\2y-2+y=4\\3y=6\\y=2\] Now you the y value is 2. Now go back in one of the equations, put 2 where y is and solve for x.