For #2x+4y=10# and #2x+4y=-10#, there is/are 1. 1 solution, 2. 2 solutions, 3. infinitely many solutions, 4. no solutions?

2 Answers

No solution - the lines are parallel


Let's graph the two of them and see what happens:

graph{(2x+4y-10)(2x+4y+10)=0 [-18.02, 18.02, -9.01, 9.01]}

They are parallel lines and so it's option 4 - no solution.


Let's look at these equations a different way. I'm going to change them into slope-intercept form, where the general formula is:

#y=mx+b; m="slope", b=y"-intercept"#



And so we can see that the slope of these two lines is the same by the point where they intersect the #y# axis is different, just as shown in the graph.

Mar 24, 2017

4) There is no solution.


Just by looking at the given equations you should be able to see that there is a problem with the equations:

Both left sides of the equations are equal, but the right sides are not:

#color(red)(2x +4y) = color(lime)(10)#
#color(red)(2x +4y)= color(magenta)(-10)#

It is not possible to add 2 identical terms and get different answers.

If#" "2x +4y = 2x+4y#

Then#" " 10= -10" "larr# this is clearly false

This indicates that there is no solution for the system of equations.