What value of b will cause the system to have an infinite number of solutions? y = 6x – b –3x + startfraction one-half endfractiony = –3 b =

The answer is 6.

Step-by-step explanation:

Equation A:

y=6x-b

Equation B:

-3x+1/2y= -3

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

We will take equation B and move all the values to the R.H.S and isolate variable y

-3x+1/2y = -3

1/2y= -3 +3x

Multiply both sides by 2

2 * 1/2y = 2(-3+3x)

y = -6+6x

y = 6x-6 Equation B(I)

Now equate Equation A and Equation B(I)

6x-b = 6x-6

Subtract 6x from both sides.

6x-6x-b = 6x-6x - 6

-b = -6

Negative sign will be cancelled out by each other.

b = 6

Thus the answer is 6...

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

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step-by-step explanation: