SOLUTION: Find two numbers a and b such that the following system of linear equations is inconsistent. ax-5y=b -4x+2y=3

Algebra ->  Linear-equations -> SOLUTION: Find two numbers a and b such that the following system of linear equations is inconsistent. ax-5y=b -4x+2y=3      Log On


   

Question 1147352: Find two numbers a and b such that the following system of linear equations is inconsistent.
ax-5y=b
-4x+2y=3
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+ax+-+5y+=+b+
+-4x+%2B+2y+=+3+
The lines are parallel, so both have the same slope
+2y+=+4x+%2B+3+
+y+=+2x+%2B+3%2F2+
This is in the form +y+=+m%2Ax+%2B+b+ where +m+ is the slope, so
+m+=+2+
---------------------
+ax+-+5y+=+b+
+5y+=+ax+-+b+
+y+=+%28+a%2F5+%29%2Ax+-+b%2F5+
-----------------------------
+a%2F5+=+2+
+a+=+10+
------------------
+b+ can be any value, since +-b%2F5+ is the y-intercept
and has no effect on the slope
-------------------------------
Here's the plots for +a=10+ and +b=10+
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x+-+2%2C+2x+%2B+3%2F2+%29+