If a question from the TASC Math exam asks you to solve for the solution to a system of equations, one useful approach is to graph the system of equations.

Graphically, the solution is the point or points where the lines or curves intersect. This means to solve a system of equations (linear, quadratic, and so on) by graphing, you follow these steps:

  1. Graph each function independently but on the same coordinate plane.
  2. Look for the point or points where the functions intersect.
  3. Test the points you identified by substituting them into all original equations. While this step is optional, it's highly recommended because graphs can be drawn inaccurately if generated by hand.

Practice question

  1. Which system of equations is represented by the following graph?
    A. y = 2x – 1; y = x + 3 B. y = –2x + 3; y = x – 1 C. y = –x + 3; y = 2x – 1 D. y = –x –1; y = 2x + 3

Answer and explanation

  1. The correct answer is Choice (B). The first thing to do is identify the y-intercepts: 3 and –1. Now find the slopes of the lines associated with each of the y-intercepts; the line with a y-intercept of 3 has a negative slope, which eliminates Choices (A) and (C). Further inspection allows you to conclude that the slope associated with 3 is –2, while the slope of the line with the y-intercept of –1 is 1. This means the equation of the two lines is y = –2x + 3 and y = x – 1, which is Choice (B).

About This Article

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About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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