Algebra · Chapter 4 of 20

Systems

68 curated · 1,228 from open sources · 957.4 million generated

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957.4 million

Endless problems made on demand, each with an exactly computed answer. Every click is a new one.

Two equations, two unknownsMedium · 957.4 million variations

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#	Title	Difficulty	Source	Tags
104	Three pairwise sums	Easy	Lemma	Adding equationsSymmetry
744	Sum and difference	Easy	Lemma	Systems
745	Substitute	Easy	Lemma	Systems
746	Line meets parabola	Easy	Lemma	Systems
1303	Nonlinear Simultaneous Equations	Easy	Hall & Knight	simultaneous equationssubstitution method
1304	Simultaneous Equations with Quadratic	Easy	Hall & Knight	simultaneous equationssubstitution method
1318	Reciprocal Fractions System	Easy	Hall & Knight	simultaneous equationsfractional equations
1319	Sum of Cubes over Product System	Easy	Hall & Knight	simultaneous equationsalgebraic manipulation
1320	Linear and Reciprocal Mixed System	Easy	Hall & Knight	simultaneous equationsreciprocal substitution
944	Solving a mixed linear‑cubic system	Medium	Hall & Knight	linear equationscubic substitution
945	Linear and cubic equations with a sum condition	Medium	Hall & Knight	substitutioncubic equation
946	Quadratic‑type relations in three variables	Medium	Hall & Knight	eliminationlinear combination
947	Quadratic forms with a linear constraint	Medium	Hall & Knight	quadratic eliminationlinear substitution
974	Composition of Brass and Bronze	Medium	Hall & Knight	mixturesratios+1
975	Rowing Stream Times	Medium	Hall & Knight	word problemsspeed and distance+1
994	Pension Proportions and Service Lengths	Medium	Hall & Knight	VariationSimultaneous Equations
1305	Homogeneous Quadratic System	Medium	Hall & Knight	simultaneous equationshomogeneous equations
1306	Symmetric Quartic System	Medium	Hall & Knight	simultaneous equationsfactoring polynomials
1307	System with Square Roots	Medium	Hall & Knight	simultaneous equationssubstitution
1308	Symmetric Radical System	Medium	Hall & Knight	simultaneous equationssymmetric equations
1309	Symmetric Radical System	Medium	Hall & Knight	systems of equationsradicals+1
1310	Homogeneous Quadratic System	Medium	Hall & Knight	systems of equationsquadratic equations
1311	Simultaneous Quadratics	Medium	Hall & Knight	systems of equationsquadratic systems
1312	Non-linear Equation System	Medium	Hall & Knight	systems of equationsquadratic equations
1313	Quadratic Equations in Two Variables	Medium	Hall & Knight	systems of equationsquadratic systems
1315	Symmetric Quartic System	Medium	Hall & Knight	simultaneous equationssymmetric polynomials+1
1316	Quartic Difference System	Medium	Hall & Knight	simultaneous equationschange of variables+1
1317	Quintic Difference System	Medium	Hall & Knight	simultaneous equationspolynomial factorization+1
1321	System with Cube Roots	Medium	Hall & Knight	simultaneous equationsradical equations
1323	Square Roots and Negative Powers	Medium	Hall & Knight	simultaneous equationsnegative exponents
1324	Radicals and Difference of Squares	Medium	Hall & Knight	radical equationssimultaneous equations
1326	Reciprocal Square Roots	Medium	Hall & Knight	simultaneous equationsrational equations
1327	System with square roots	Medium	Hall & Knight	simultaneous equationsradical equations
1328	Quadratic and product system	Medium	Hall & Knight	simultaneous equationssubstitution
1330	Linear and quadratic combination	Medium	Hall & Knight	simultaneous equationssubstitution
1333	System of Homogeneous Quadratic Equations	Medium	Hall & Knight	simultaneous equationshomogeneous equations
1334	Algebraic Fraction and Linear Equation System	Medium	Hall & Knight	simultaneous equationsalgebraic fractions
1342	Homogeneous and Quadratic System	Medium	Hall & Knight	systems of equationshomogeneous equations+1
1343	Linear and Cubic System	Medium	Hall & Knight	systems of equationscubic equations+1
1344	Mixed Algebraic System	Medium	Hall & Knight	systems of equationsnonlinear systems
1345	Linear and Quadratic Product System	Medium	Hall & Knight	systems of equationsquadratic systems
1347	Three Symmetric Quadratic Equations	Medium	Hall & Knight	systems of equationssymmetric equations
1348	Homogeneous and Linear Systems	Medium	Hall & Knight	simultaneous equationshomogeneous equations
1349	Cyclic Product Equations	Medium	Hall & Knight	simultaneous equationsproduct of differences
1350	Exponential Product System	Medium	Hall & Knight	simultaneous equationsproduct systems
1351	Power Product System	Medium	Hall & Knight	simultaneous equationsexponents
1352	Symmetric Product-Sum Equations	Medium	Hall & Knight	simultaneous equationsfactorisation
1353	Bilinear Variable Systems	Medium	Hall & Knight	simultaneous equationsfactorisation
1354	System of Three Variables	Medium	Hall & Knight	simultaneous equationssubstitution
1355	Symmetric Cubic System	Medium	Hall & Knight	symmetric polynomialspower sums
1314	Simultaneous Quadratic Equations	Deep	Hall & Knight	systems of equationsquadratic systems+1
1322	Fractional Exponent System	Deep	Hall & Knight	simultaneous equationsfractional exponents
1325	Nested Radicals and Square Roots	Deep	Hall & Knight	radical equationssimultaneous equations
1329	Homogeneous and product forms	Deep	Hall & Knight	simultaneous equationshomogeneous equations
1331	Nonlinear system with complex roots	Deep	Hall & Knight	simultaneous equationscomplex roots
1332	Difference of powers system	Deep	Hall & Knight	simultaneous equationsalgebraic manipulation
1335	Cubic Homogeneous System	Deep	Hall & Knight	simultaneous equationshomogeneous equations
1336	Cubic Equations with Constant Term	Deep	Hall & Knight	simultaneous equationshomogeneous systems
1337	Nonlinear Symmetric System	Deep	Hall & Knight	simultaneous equationshigher degree equations
1338	System of Quadratic Equations	Deep	Hall & Knight	systems of equationsquadratic equations
1339	Nonlinear System with Products	Deep	Hall & Knight	systems of equationsnon-linear equations
1340	Fractional Equations with Parameters	Deep	Hall & Knight	fractional equationsalgebraic manipulation
1341	Homogeneous Cubic System	Deep	Hall & Knight	cubic equationshomogeneous equations
1346	Symmetric Quadratic and Linear System	Deep	Hall & Knight	systems of equationsquadratic systems
1356	Quadratic and Linear System with Parameter	Deep	Hall & Knight	homogeneous equationsquadratic systems
1357	Complex Solutions for Three Variables	Deep	Hall & Knight	simultaneous equationscomplex roots
1902	Symmetric Equal Products	Deep	Hall & Knight	systems of equationssymmetry
1903	Real Triads of Solutions	Deep	Hall & Knight	linear systemsdeterminants+1

From open sources

1,228

Showing everything, including problems with no answer to check, a missing figure, or a near-copy elsewhere. Show only complete problems

#	Title	Difficulty
104968	Systems of Linear Equations: Two Variables · Example 1	Easy
104973	Determining Whether an Ordered Pair Is a Solution to a System of Equations	Easy
104977	Solving a System of Equations in Two Variables by Substitution	Easy
104979	Solving a System by the Addition Method	Easy
104983	Using the Addition Method in Systems of Equations Containing Fractions	Easy
104985	Solving an Inconsistent System of Equations	Easy
104987	Finding a Solution to a Dependent System of Linear Equations	Easy
104988	Systems of Linear Equations: Two Variables · Try It 7	Easy
104989	Finding the Break-Even Point and the Profit Function Using Substitution	Easy
104990	Writing and Solving a System of Equations in Two Variables	Easy
104992	Systems of Linear Equations: Two Variables · Exercise 5	Easy
104994	Systems of Linear Equations: Two Variables · Exercise 7	Easy
104996	Systems of Linear Equations: Two Variables · Exercise 9	Easy
105046	Systems of Linear Equations: Two Variables · Exercise 59	Deep
105064	Systems of Linear Equations: Two Variables · Exercise 77	Medium
105069	Systems of Linear Equations: Three Variables · Example 1	Easy
105075	Determining Whether an Ordered Triple Is a Solution to a System	Easy
105077	Solving a Real-World Problem Using a System of Three Equations in Three Variables	Easy
105079	Solving an Inconsistent System of Three Equations in Three Variables	Easy
105081	Finding the Solution to a Dependent System of Equations	Easy
105082	Systems of Linear Equations: Three Variables · Try It 4	Easy
105083	Systems of Linear Equations: Three Variables · Exercise 4	Easy
105085	Systems of Linear Equations: Three Variables · Exercise 6	Easy
105087	Systems of Linear Equations: Three Variables · Exercise 8	Easy
105095	Systems of Linear Equations: Three Variables · Exercise 16	Medium
105101	Systems of Linear Equations: Three Variables · Exercise 22	Medium
105129	Systems of Linear Equations: Three Variables · Exercise 50	Deep
105137	Systems of Linear Equations: Three Variables · Exercise 58	Medium
105139	Systems of Linear Equations: Three Variables · Exercise 60	Medium
105143	Systems of Linear Equations: Three Variables · Exercise 64	Medium
105145	Systems of Linear Equations: Three Variables · Exercise 66	Medium
105147	Systems of Linear Equations: Three Variables · Exercise 68	Medium
105149	Systems of Linear Equations: Three Variables · Exercise 70	Medium
105151	Systems of Linear Equations: Three Variables · Exercise 72	Medium
105156	Systems of Nonlinear Equations and Inequalities: Two Variables · Try It 1	Easy
105160	Systems of Nonlinear Equations and Inequalities: Two Variables · Try It 3	Easy
105164	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 4	Easy
105166	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 6	Easy
105168	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 8	Easy
105175	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 16	Medium
105177	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 18	Medium
105181	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 22	Medium
105193	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 34	Medium
105197	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 38	Medium
105199	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 40	Medium
105211	Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 52	Deep
117841	Solve Systems of Equations by Graphing · Example 9	Easy
117844	Solve Systems of Equations by Graphing · Example 10	Easy
117847	Solve Systems of Equations by Graphing · Example 11	Easy
117914	Solve Systems of Equations by Graphing · Exercise 63	Easy