Answer:
[tex]b=6[/tex]
Step-by-step explanation:
The correct question is
What value of b will cause the system to have an infinite number of solutions?
y = 6x – b
–3x + 1/2y = –3
we have
[tex]y=6x-b[/tex] ----->equation A
[tex]-3x+\frac{1}{2}y=-3[/tex] -----> equation B
we know that
If the system has infinite number of solutions then, the equation A must be equal to the equation B
so
isolate variable y in the equation B
[tex]-3x+\frac{1}{2}y=-3[/tex]
Multiply by [tex]2[/tex] both sides
[tex]-6x+y=-6[/tex]
[tex]y=6x-6[/tex] -------> new equation B
To find out the value of b, equate equation A and equation B
[tex]6x-b=6x-6[/tex]
[tex]b=6[/tex]
