Question

Which graph shows a system of equations that solves −
2
x − 1
= 4, and the solution itself?


mc001-1.jpg

mc001-2.jpg

mc001-3.jpg

Answer 1

Interpret the equation as −2/(x − 1) = 4. Graph it as a system:
y = −2/(x − 1) and y = 4.

Solve algebraically:
−2/(x − 1) = 4
−2 = 4(x − 1)
−2 = 4x − 4
4x = 2
x = 1/2.

So the solution (intersection) is (1/2, 4). Pick the image that shows the hyperbola y = −2/(x−1) with vertical asymptote x = 1 together with the horizontal line y = 4, intersecting at x = 0.5.