plz help with systems
For certain values of k and m, the system
3a + 2b = 2
6a + 2b = k + 3a + mb
has infinitely many solutions (a,b). What are k and m?
+120 To have something that has infinite solutions we need both sides of a equation to be the exact same. Now lets use this to our advantage.
Let us simply the system of equations via substitution :
3a + 2b = 2
= 3a = 2 - 2b
Now we can substitute that into the second equation :
6a + 2b = k + 3a + mb
= (2 - 2b) x 2 + 2b = k + ( 2 - 2b ) + mb
= 4 - 4b + 2b = k + 2 -2b + mb
= 4 - 2b = k + 2-2b + mb
Now after this, we will start moving variables :
4 = 2 + mb + k
2 = mb + k
Now you may feel stuck at this point but we will need to use guess and check to find the answer :
Since 2 is such a small number I would assume in this problem that some variable would be equal to 0
Using substituion we can find the m = 0 and k = 2
Hope this helps!
