How many solutions does the system of equations #7x + y = 1# and #14x + 2y = 17# have?

1 Answer
Jun 9, 2017

No real solutions

Explanation:

Rewrite both equations in slope-intercept form:

For the first equation:

#y=-7x+1#

For the second equation:

#y=-7x+17#

We can see that they have the same slope and different y-intercepts. That means they're parallel lines and never cross.

However, just to be sure, we can set the two equations together and attempt to solve for #x#:

#-7x+1=-7x+17#

Subtract #1# on both sides:

#-7x+1-1=-7x+17-1#

This gives you:

#-7x=-7x+16#

Now move all the #x#s on one side. Add #7x# to both sides.

#-7x=-7x+16+7x#

This gives:

#0=16#

Obviously, this statement is false. That means that the graphs never touch. If the two equal each other, then the graphs will always touch.