System of equations — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses system of equations — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All of these problems are used with official legal permission of the Mathematical Association of America (MAA).
AMC 8
1990 AMC 8 Problem 24 · 2003 AMC 8 Problem 4 · 2008 AMC 8 Problem 13 · 2012 AMC 8 Problem 9 · 2012 AMC 8 Problem 19 · 2015 AMC 8 Problem 20 · 2017 AMC 8 Problem 17 · 2019 AMC 8 Problem 21 · 2020 AMC 8 Problem 25 · 2022 AMC 8 Problem 16 · 2026 AMC 8 Problem 14
AMC 10
2000 AMC 10 Problem 4 · 2000 AMC 10 Problem 16 · 2001 AMC 10 Problem 10 · 2002 AMC 10A Problem 9 · 2002 AMC 10A Problem 16 · 2002 AMC 10B Problem 10 · 2002 AMC 10B Problem 20 · 2002 AMC 10B Problem 22 · 2002 AMC 10B Problem 25 · 2003 AMC 10A Problem 13 · 2003 AMC 10B Problem 12 · 2003 AMC 10B Problem 24 · 2004 AMC 10B Problem 15 · 2006 AMC 10A Problem 8 · 2006 AMC 10B Problem 3 · 2006 AMC 10B Problem 12 · 2006 AMC 10B Problem 23 · 2007 AMC 10A Problem 5 · 2007 AMC 10A Problem 9 · 2008 AMC 10A Problem 15 · 2008 AMC 10A Problem 18 · 2008 AMC 10B Problem 11 · 2009 AMC 10B Problem 15 · 2011 AMC 10B Problem 21 · 2012 AMC 10A Problem 6 · 2012 AMC 10A Problem 8 · 2012 AMC 10A Problem 19 · 2014 AMC 10A Problem 25 · 2014 AMC 10B Problem 4 · 2015 AMC 10A Problem 2 · 2015 AMC 10A Problem 8 · 2015 AMC 10A Problem 16 · 2016 AMC 10B Problem 11 · 2016 AMC 10B Problem 13 · 2017 AMC 10A Problem 14 · 2017 AMC 10B Problem 5 · 2017 AMC 10B Problem 10 · 2017 AMC 10B Problem 13 · 2018 AMC 10A Problem 8 · 2018 AMC 10A Problem 12 · 2018 AMC 10B Problem 4 · 2019 AMC 10A Problem 3 · 2019 AMC 10B Problem 11 · 2019 AMC 10B Problem 15 · 2020 AMC 10A Problem 13 · 2021 AMC 10B Spring Problem 3 · 2021 AMC 10B Spring Problem 13 · 2021 AMC 10B Spring Problem 19 · 2021 AMC 10A Fall Problem 14 · 2021 AMC 10A Fall Problem 17 · 2022 AMC 10A Problem 3 · 2022 AMC 10B Problem 18 · 2022 AMC 10B Problem 21 · 2023 AMC 10A Problem 10 · 2023 AMC 10B Problem 5 · 2024 AMC 10A Problem 2 · 2024 AMC 10A Problem 21 · 2024 AMC 10A Problem 23 · 2025 AMC 10A Problem 4 · 2025 AMC 10A Problem 7 · 2025 AMC 10B Problem 24
AMC 12
1999 AMC 12 Problem 17 · 1999 AMC 12 Problem 27 · 1999 AMC 12 Problem 28 · 2000 AMC 12 Problem 20 · 2001 AMC 12 Problem 21 · 2002 AMC 12A Problem 11 · 2002 AMC 12B Problem 19 · 2003 AMC 12B Problem 2 · 2003 AMC 12B Problem 7 · 2003 AMC 12B Problem 17 · 2003 AMC 12B Problem 24 · 2004 AMC 12A Problem 19 · 2004 AMC 12B Problem 13 · 2004 AMC 12B Problem 22 · 2006 AMC 12A Problem 13 · 2006 AMC 12B Problem 3 · 2006 AMC 12B Problem 8 · 2008 AMC 12A Problem 18 · 2009 AMC 12A Problem 8 · 2009 AMC 12B Problem 8 · 2010 AMC 12A Problem 10 · 2011 AMC 12A Problem 6 · 2011 AMC 12A Problem 20 · 2011 AMC 12B Problem 13 · 2012 AMC 12A Problem 5 · 2012 AMC 12A Problem 6 · 2012 AMC 12A Problem 13 · 2012 AMC 12A Problem 21 · 2012 AMC 12B Problem 9 · 2012 AMC 12B Problem 10 · 2012 AMC 12B Problem 17 · 2013 AMC 12A Problem 11 · 2013 AMC 12B Problem 10 · 2014 AMC 12A Problem 11 · 2014 AMC 12A Problem 22 · 2014 AMC 12B Problem 16 · 2015 AMC 12A Problem 6 · 2015 AMC 12A Problem 20 · 2016 AMC 12B Problem 4 · 2016 AMC 12B Problem 9 · 2017 AMC 12A Problem 13 · 2018 AMC 12A Problem 6 · 2018 AMC 12A Problem 10 · 2019 AMC 12A Problem 12 · 2019 AMC 12B Problem 21 · 2020 AMC 12A Problem 11 · 2020 AMC 12B Problem 5 · 2021 AMC 12A Spring Problem 6 · 2021 AMC 12A Spring Problem 21 · 2021 AMC 12B Spring Problem 12 · 2022 AMC 12A Problem 2 · 2023 AMC 12A Problem 8 · 2023 AMC 12A Problem 9 · 2023 AMC 12A Problem 10 · 2023 AMC 12B Problem 12 · 2024 AMC 12A Problem 2 · 2024 AMC 12A Problem 14 · 2024 AMC 12A Problem 17 · 2025 AMC 12A Problem 3 · 2025 AMC 12A Problem 7 · 2025 AMC 12B Problem 20
AIME
2000 AIME I Problem 4 · 2000 AIME I Problem 7 · 2000 AIME I Problem 9 · 2000 AIME I Problem 10 · 2001 AIME I Problem 2 · 2001 AIME I Problem 11 · 2001 AIME II Problem 4 · 2003 AIME II Problem 8 · 2004 AIME II Problem 6 · 2006 AIME I Problem 5 · 2006 AIME II Problem 15 · 2007 AIME II Problem 4 · 2008 AIME I Problem 3 · 2008 AIME I Problem 13 · 2009 AIME I Problem 14 · 2010 AIME I Problem 9 · 2012 AIME I Problem 7 · 2012 AIME II Problem 4 · 2012 AIME II Problem 8 · 2013 AIME II Problem 13 · 2014 AIME I Problem 4 · 2014 AIME I Problem 13 · 2014 AIME II Problem 5 · 2015 AIME I Problem 10 · 2016 AIME II Problem 1 · 2016 AIME II Problem 3 · 2018 AIME II Problem 5 · 2018 AIME II Problem 12 · 2018 AIME II Problem 13 · 2019 AIME II Problem 6 · 2020 AIME II Problem 11 · 2021 AIME II Problem 7 · 2022 AIME I Problem 15 · 2023 AIME II Problem 4 · 2024 AIME II Problem 4 · 2026 AIME I Problem 1