m-c-mc-7-3equationgraph_resize

table row cell x squared end cell plus cell y squared end cell equals 5 row y equals cell x squared end cell minus 3 row x minus y equals 1 end table

A system of three equations and their graphs in the xy-plane are shown above. How many solutions does the system have?

  • A. One.
  • B. Two.
  • C. Three.
  • D. Four.

Answer: B

Why? 

The solutions to the system of equations are the points where the circle, parabola, and line all intersect. These points are open parentheses minus 1 comma 2 close parentheses and left parenthesis 2 comma 1 right parenthesis, and these are the only solutions to the system.

Question Difficulty: EASY

Objective: Students must demonstrate their conceptual understanding of graphical representations of variable relationships.

Words:
  1. graphs – đồ thị (n): a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
  2. xy-plane – trục xy (n): A plane with x- and y-axes defined is often referred to as the Cartesian plane or xyplane. The value of x is called the x-coordinate or abscissa and the value of y is called the y-coordinate or ordinate.

 

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