What value of b will cause the system to have an infinite number of solutions? y = 6x – b –3x + 1/2y = –3

we have

-----> equation A

-----> equation B

we know that

If the system has infinite number of solutions then, the equation A is equal to the equation B

so

isolate variable y in the equation B

Multiply by both sides

-------> new equation B

To find the value of b, equate equation A and equation B

therefore

the answer is

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places