Lemma

Algebra · Chapter 4 of 20

Systems

68 curated · 566 from open sources · 957.4 million generated

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Two equations, two unknownsMedium · 957.4 million variations

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68
#TitleDifficultySourceTags
104Three pairwise sumsEasyLemmaAdding equationsSymmetry
744Sum and differenceEasyLemmaSystems
745SubstituteEasyLemmaSystems
746Line meets parabolaEasyLemmaSystems
1303Nonlinear Simultaneous EquationsEasyHall & Knightsimultaneous equationssubstitution method
1304Simultaneous Equations with QuadraticEasyHall & Knightsimultaneous equationssubstitution method
1318Reciprocal Fractions SystemEasyHall & Knightsimultaneous equationsfractional equations
1319Sum of Cubes over Product SystemEasyHall & Knightsimultaneous equationsalgebraic manipulation
1320Linear and Reciprocal Mixed SystemEasyHall & Knightsimultaneous equationsreciprocal substitution
944Solving a mixed linear‑cubic systemMediumHall & Knightlinear equationscubic substitution
945Linear and cubic equations with a sum conditionMediumHall & Knightsubstitutioncubic equation
946Quadratic‑type relations in three variablesMediumHall & Knighteliminationlinear combination
947Quadratic forms with a linear constraintMediumHall & Knightquadratic eliminationlinear substitution
974Composition of Brass and BronzeMediumHall & Knightmixturesratios+1
975Rowing Stream TimesMediumHall & Knightword problemsspeed and distance+1
994Pension Proportions and Service LengthsMediumHall & KnightVariationSimultaneous Equations
1305Homogeneous Quadratic SystemMediumHall & Knightsimultaneous equationshomogeneous equations
1306Symmetric Quartic SystemMediumHall & Knightsimultaneous equationsfactoring polynomials
1307System with Square RootsMediumHall & Knightsimultaneous equationssubstitution
1308Symmetric Radical SystemMediumHall & Knightsimultaneous equationssymmetric equations
1309Symmetric Radical SystemMediumHall & Knightsystems of equationsradicals+1
1310Homogeneous Quadratic SystemMediumHall & Knightsystems of equationsquadratic equations
1311Simultaneous QuadraticsMediumHall & Knightsystems of equationsquadratic systems
1312Non-linear Equation SystemMediumHall & Knightsystems of equationsquadratic equations
1313Quadratic Equations in Two VariablesMediumHall & Knightsystems of equationsquadratic systems
1315Symmetric Quartic SystemMediumHall & Knightsimultaneous equationssymmetric polynomials+1
1316Quartic Difference SystemMediumHall & Knightsimultaneous equationschange of variables+1
1317Quintic Difference SystemMediumHall & Knightsimultaneous equationspolynomial factorization+1
1321System with Cube RootsMediumHall & Knightsimultaneous equationsradical equations
1323Square Roots and Negative PowersMediumHall & Knightsimultaneous equationsnegative exponents
1324Radicals and Difference of SquaresMediumHall & Knightradical equationssimultaneous equations
1326Reciprocal Square RootsMediumHall & Knightsimultaneous equationsrational equations
1327System with square rootsMediumHall & Knightsimultaneous equationsradical equations
1328Quadratic and product systemMediumHall & Knightsimultaneous equationssubstitution
1330Linear and quadratic combinationMediumHall & Knightsimultaneous equationssubstitution
1333System of Homogeneous Quadratic EquationsMediumHall & Knightsimultaneous equationshomogeneous equations
1334Algebraic Fraction and Linear Equation SystemMediumHall & Knightsimultaneous equationsalgebraic fractions
1342Homogeneous and Quadratic SystemMediumHall & Knightsystems of equationshomogeneous equations+1
1343Linear and Cubic SystemMediumHall & Knightsystems of equationscubic equations+1
1344Mixed Algebraic SystemMediumHall & Knightsystems of equationsnonlinear systems
1345Linear and Quadratic Product SystemMediumHall & Knightsystems of equationsquadratic systems
1347Three Symmetric Quadratic EquationsMediumHall & Knightsystems of equationssymmetric equations
1348Homogeneous and Linear SystemsMediumHall & Knightsimultaneous equationshomogeneous equations
1349Cyclic Product EquationsMediumHall & Knightsimultaneous equationsproduct of differences
1350Exponential Product SystemMediumHall & Knightsimultaneous equationsproduct systems
1351Power Product SystemMediumHall & Knightsimultaneous equationsexponents
1352Symmetric Product-Sum EquationsMediumHall & Knightsimultaneous equationsfactorisation
1353Bilinear Variable SystemsMediumHall & Knightsimultaneous equationsfactorisation
1354System of Three VariablesMediumHall & Knightsimultaneous equationssubstitution
1355Symmetric Cubic SystemMediumHall & Knightsymmetric polynomialspower sums
1314Simultaneous Quadratic EquationsDeepHall & Knightsystems of equationsquadratic systems+1
1322Fractional Exponent SystemDeepHall & Knightsimultaneous equationsfractional exponents
1325Nested Radicals and Square RootsDeepHall & Knightradical equationssimultaneous equations
1329Homogeneous and product formsDeepHall & Knightsimultaneous equationshomogeneous equations
1331Nonlinear system with complex rootsDeepHall & Knightsimultaneous equationscomplex roots
1332Difference of powers systemDeepHall & Knightsimultaneous equationsalgebraic manipulation
1335Cubic Homogeneous SystemDeepHall & Knightsimultaneous equationshomogeneous equations
1336Cubic Equations with Constant TermDeepHall & Knightsimultaneous equationshomogeneous systems
1337Nonlinear Symmetric SystemDeepHall & Knightsimultaneous equationshigher degree equations
1338System of Quadratic EquationsDeepHall & Knightsystems of equationsquadratic equations
1339Nonlinear System with ProductsDeepHall & Knightsystems of equationsnon-linear equations
1340Fractional Equations with ParametersDeepHall & Knightfractional equationsalgebraic manipulation
1341Homogeneous Cubic SystemDeepHall & Knightcubic equationshomogeneous equations
1346Symmetric Quadratic and Linear SystemDeepHall & Knightsystems of equationsquadratic systems
1356Quadratic and Linear System with ParameterDeepHall & Knighthomogeneous equationsquadratic systems
1357Complex Solutions for Three VariablesDeepHall & Knightsimultaneous equationscomplex roots
1902Symmetric Equal ProductsDeepHall & Knightsystems of equationssymmetry
1903Real Triads of SolutionsDeepHall & Knightlinear systemsdeterminants+1

From open sources

566

Complete problems only, with worked solutions first. Show everything

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