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 problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
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
1950 AMC 12 Problem 6 • 1950 AMC 12 Problem 14 • 1950 AMC 12 Problem 30 • 1951 AMC 12 Problem 35 • 1951 AMC 12 Problem 44 • 1951 AMC 12 Problem 49 • 1951 AMC 12 Problem 50 • 1952 AMC 12 Problem 47 • 1953 AMC 12 Problem 8 • 1954 AMC 12 Problem 12 • 1954 AMC 12 Problem 30 • 1954 AMC 12 Problem 48 • 1957 AMC 12 Problem 23 • 1957 AMC 12 Problem 41 • 1959 AMC 12 Problem 17 • 1960 AMC 12 Problem 5 • 1960 AMC 12 Problem 18 • 1960 AMC 12 Problem 29 • 1960 AMC 12 Problem 30 • 1961 AMC 12 Problem 26 • 1962 AMC 12 Problem 19 • 1963 AMC 12 Problem 16 • 1964 AMC 12 Problem 11 • 1964 AMC 12 Problem 18 • 1964 AMC 12 Problem 19 • 1964 AMC 12 Problem 23 • 1964 AMC 12 Problem 25 • 1965 AMC 12 Problem 28 • 1965 AMC 12 Problem 38 • 1966 AMC 12 Problem 16 • 1966 AMC 12 Problem 17 • 1966 AMC 12 Problem 27 • 1966 AMC 12 Problem 37 • 1966 AMC 12 Problem 39 • 1967 AMC 12 Problem 10 • 1967 AMC 12 Problem 19 • 1968 AMC 12 Problem 13 • 1968 AMC 12 Problem 14 • 1968 AMC 12 Problem 32 • 1968 AMC 12 Problem 34 • 1969 AMC 12 Problem 4 • 1969 AMC 12 Problem 18 • 1969 AMC 12 Problem 34 • 1970 AMC 12 Problem 11 • 1970 AMC 12 Problem 19 • 1970 AMC 12 Problem 26 • 1970 AMC 12 Problem 32 • 1970 AMC 12 Problem 35 • 1972 AMC 12 Problem 9 • 1972 AMC 12 Problem 11 • 1972 AMC 12 Problem 16 • 1972 AMC 12 Problem 24 • 1973 AMC 12 Problem 10 • 1973 AMC 12 Problem 14 • 1973 AMC 12 Problem 24 • 1973 AMC 12 Problem 26 • 1973 AMC 12 Problem 33 • 1973 AMC 12 Problem 34 • 1975 AMC 12 Problem 2 • 1977 AMC 12 Problem 21 • 1978 AMC 12 Problem 6 • 1978 AMC 12 Problem 13 • 1978 AMC 12 Problem 20 • 1980 AMC 12 Problem 11 • 1980 AMC 12 Problem 12 • 1980 AMC 12 Problem 19 • 1981 AMC 12 Problem 17 • 1982 AMC 12 Problem 15 • 1983 AMC 12 Problem 1 • 1983 AMC 12 Problem 13 • 1986 AMC 12 Problem 6 • 1986 AMC 12 Problem 12 • 1987 AMC 12 Problem 10 • 1987 AMC 12 Problem 15 • 1990 AMC 12 Problem 15 • 1990 AMC 12 Problem 20 • 1990 AMC 12 Problem 24 • 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
1984 AIME Problem 5 • 1985 AIME Problem 5 • 1985 AIME Problem 9 • 1986 AIME Problem 4 • 1986 AIME Problem 10 • 1986 AIME Problem 14 • 1987 AIME Problem 6 • 1987 AIME Problem 10 • 1988 AIME Problem 6 • 1988 AIME Problem 13 • 1989 AIME Problem 7 • 1989 AIME Problem 8 • 1989 AIME Problem 14 • 1990 AIME Problem 15 • 1991 AIME Problem 1 • 1992 AIME Problem 4 • 1993 AIME Problem 3 • 1996 AIME Problem 1 • 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