+17 For a certain value of the system:
\(3a+4b = 7,\)
\(6a+4b = k-4b\)
has infinitely many solutions (a, b). What is \(k\)?
+2668 Simplify the second equation to: \(6a+8 b=k\).
For a system of equations to have infinite solutions, the two equations must be a multiple of each other.
Note that the second equation is twice the first equation.
Can you take it from here?
+186 k=14
Explanation:
First, put the like terms on the same side. 6a+4b=k-4b turns into 6a+8b=k
Then you can multiply the top equation by 2 to get 6a+8b=14
Now, you have the system of linear equations,
{6a+8b=14,
{6a+8b=k
Therefore, k must be equal to 14.
