Ada draws the graph of y = x2 - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?

Step 1: Analyze the question When two graphs are drawn on the same axes, their points of intersection give the solution to the equation formed by setting the two expressions for y equal to each other.

Step 2: Set the equations equal x² - x - 2 = 2x - 1

Step 3: Move everything to one side Subtract 2x from both sides and add 1 to both sides:

x² - x - 2 - 2x + 1 = 0

x² - 3x - 1 = 0

Step 4: Check against the options This matches option B: x² - 3x - 1 = 0.

Why the others are wrong:

• A: x² - x - 3 = 0 only subtracts 1 from the constant and never moves 2x across.
• C: x² - 3x - 3 = 0 combines the constants wrongly (-2 - 1 instead of -2 + 1).
• D: x² + 3x - 1 = 0 gets the sign of the x term wrong (it should be -x - 2x = -3x).

Exam tip: To find the equation solved by two graphs, always write "curve = line", then collect everything on one side so the right-hand side is 0. Watch your signs carefully when you move terms across. Subtracting a positive term (like 2x) makes it negative, and subtracting a negative constant (like -1) makes it positive.