What value of b will cause the system to have an infinite number of solutions? A system of equations. y equals 6 x plus b. negative 3 x plus StartFraction one-half EndFraction y equals negative 3.
Accepted Solution
A:
Answer:[tex]b=-6[/tex]Step-by-step explanation:we have[tex]y=6x+b[/tex] ----> equation A[tex]-3x+\frac{1}{2}y=-3[/tex] -----> equation Bwe know thatIf equation A is the same of equation B, then the system of equations will have infinite solutionsConvert equation B in slope intercept formIsolate the variable yMultiply by 2 both sides to remove the fractions[tex]-6x+y=-6[/tex] Adds 6x both sides[tex]y=6x-6[/tex] -----> equation C (slope intercept form)Equate equation A and equation C and solve for b[tex]6x+b=6x-6[/tex] [tex]b=-6[/tex]