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
Explanation:
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.
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Let's look at these equations a different way. I'm going to change them into slope-intercept form, where the general formula is:
And so we can see that the slope of these two lines is the same by the point where they intersect the
4) There is no solution.
Explanation:
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:
It is not possible to add 2 identical terms and get different answers.
Mathematically:
If
Then
This indicates that there is no solution for the system of equations.
