Question

I need help ASAP I'm failing and I'm having trouble with this assignment.

Answer 1

Answer: Choice D

(-3, -1/2)

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Step-by-step explanation:

Set the right hand sides equal to one another. This is valid since they are equal to the same variable (y).

`(1)/(2)\text{x} + 1 = (3)/(2)\text{x} + 4\\\\\text{x} + 2 = 3\text{x} + 8\\\\\text{x}-3\text{x} = 8-2\\\\-2\text{x} = 6\\\\\text{x} = 6/(-2)\\\\\text{x} = -3\\\\`

In the 2nd step, I multiplied each term by 2 to clear out the fractions.

Then use this x value to find y.

Plug x = -3 into either of the original equations.

`\begin{array}l\text{Option 1} & \text{Option 2}\\\cline{1-2}\\\text{y} = (1)/(2)\text{x} + 1 & \text{y} = (3)/(2)\text{x} + 4\\\\\text{y} = (1)/(2)*(-3) + 1 & \text{y} = (3)/(2)*(-3) + 4\\\\\text{y} = -(3)/(2) + 1 & \text{y} = -(9)/(2) + 4\\\\\text{y} = -(3)/(2) + (2)/(2) & \text{y} = -(9)/(2) + (8)/(2)\\\\\text{y} = (-3+2)/(2) & \text{y} = (-9+8)/(2)\\\\\text{y} = -(1)/(2) & \text{y} = -(1)/(2)\\\\\end{array}`

Both roads lead to the same y value. Take your pick which you prefer better. Doing both options will help you practice and it helps verify the answer.

Another way to verify is to use a graphing tool like GeoGebra or Desmos. The two lines intersect at (-3, -0.5) where -1/2 = -0.5