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?

Guest Jul 12, 2023

#1**0 **

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!**

breadstickim01 Jul 12, 2023