Hi there!
The way that an infinite number of solutions is achieved is when the two equations, when solved together, get an answer which is just a number equal to the same number. To do this, first substitute 6x-b in for y in the second equation.
[tex]-3x+\frac{1}{2}(6x-b)=-3[/tex]
[tex]-3x+3x-\frac{1}{2}b=-3[/tex]
[tex]-\frac{1}{2}b=-3[/tex]
Now, we see that b needs to be equal to -3 when multiplied by -1/2. When both sides are divided by -1/2, b becomes equal to 6. Thus, b must be 6.
Check work:
[tex]6x-6=y[/tex]
[tex]-3x+\frac{1}{2}(6x-6)=-3[/tex]
[tex]-3x+3x-3=-3[/tex]
[tex]-3=-3[/tex]
Thus, as they are equal to each other, the answer is correct. b = 6.
Hope this helps!
