温馨提示：本站仅提供公开网络链接索引服务，不存储、不篡改任何第三方内容，所有内容版权归原作者所有
AI智能索引来源：http://www.edu.com/math-glossary/Solution-Definition-Example
点击访问原文链接

Solution: Definition and Example | EDU.COM

进入原网站 导航首页
Solution: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">SolutionSolution: Definition and ExampleTable of ContentsSolution in Mathematics Definition of Solution

In mathematics, a solution\text{solution}solution is the answer to a problem or the value(s) that satisfy an equation. For example, in x+5=12x + 5 = 12x+5=12, the solution is x=7x = 7x=7 because 7+5=127 + 5 = 127+5=12. Solutions can be: Single numbers (e.g., x=7x = 7x=7), sets of numbers (e.g., x=2,3x = {2, 3}x=2,3) , functions or geometric properties.

Solutions are foundational for translating real-world problems into mathematical answers. Equations may have one solution, multiple solutions, or no solution.

Examples of Solution Example 1: Linear Equation Solution Problem:

Solve 2x−6=82x - 6 = 82x−6=8.

Step-by-step solution:

Step 1, Add 666 to both sides:

2x−6+6=8+62x - 6 + 6 = 8 + 62x−6+6=8+6 → 2x=142x = 142x=14

Step 2, Divide by 2:

2x2=142\frac{2x}{2} = \frac{14}{2}22x​=214​ → x=7x = 7x=7

Step 3, Verify: 2(7)−6=14−6=82(7) - 6 = 14 - 6 = 82(7)−6=14−6=8 ✓

Example 2: System of Equations Solution Problem:

Solve:

x+y=5x + y = 5x+y=5 2x−y=42x - y = 42x−y=4 Step-by-step solution:

Step 1, Solve first equation for yyy: y=5−xy = 5 - xy=5−x

Step 2, Substitute into second equation:

2x−(5−x)=42x - (5 - x) = 42x−(5−x)=4 → 2x−5+x=42x - 5 + x = 42x−5+x=4 → 3x=93x = 93x=9 → x=3x = 3x=3

Step 3, Find yyy: y=5−3=2y = 5 - 3 = 2y=5−3=2

Step 4, Verify:

3+2=53 + 2 = 53+2=5 ✓, 2(3)−2=42(3) - 2 = 42(3)−2=4 ✓

Solution: (x,y)=(3,2)(x, y) = (3, 2)(x,y)=(3,2)

Example 3: Quadratic Equation Solution Problem:

Solve x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0.

Step-by-step solution:

Step 1, Factor the quadratic:

x2−5x+6=(x−2)(x−3)x^2 - 5x + 6 = (x - 2)(x - 3)x2−5x+6=(x−2)(x−3)

Step 2, Apply zero-product property:

(x−2)=0(x - 2) = 0(x−2)=0 or (x−3)=0(x - 3) = 0(x−3)=0

Step 3, Solutions: x=2x = 2x=2, x=3x = 3x=3

Step 4, Verify:

22−5(2)+6=02^2 - 5(2) + 6 = 022−5(2)+6=0 ✓, 32−5(3)+6=03^2 - 5(3) + 6 = 032−5(3)+6=0 ✓

Comments(2)AArtistDianaNovember 6, 2025I've used this solution definition to help my students. It's clear and the examples really make the concept easy to grasp!

DDancerMonaNovember 4, 2025I've used this solution def to help my students. It's clear and the real-life examples make it easy for them to grasp!

Explore More TermsThousandsSegment Addition PostulateDecimalMiles to Km FormulaMultiplication on Number LineUnit CubeView All Math TermsRecommended Interactive LessonsUnderstand the Commutative Property of Multiplication3Math3.OA.B.5Equivalent Fractions of Whole Numbers on a Number Line3Math3.NF.A.3cIdentify and Describe Subtraction Patterns3Math3.OA.D.9Identify and Describe Mulitplication Patterns3Math3.OA.D.9Multiply Easily Using the Distributive Property3Math3.OA.B.5Understand Equivalent Fractions Using Pizza Models3Math3.NF.A.3.a, 3.NF.A.3.bView All Interactive LessonsRecommended VideosSubtraction Within 10KMathK.OA.A.2, K.OA.A.5Classify Quadrilaterals Using Shared Attributes3Math3.G.A.1Understand and Estimate Liquid Volume3Math3.MD.A.2Convert Units Of Time4Math4.MD.A.1，4.MD.A.2Use Models and Rules to Multiply Whole Numbers by Fractions5Math5.NF.B.4aCreate and Interpret Box Plots6Math6.SP.B.4View All VideosRecommended WorksheetsTell Time To The Half Hour: Analog and Digital Clock1Math1.MD.B.3Estimate Lengths Using Customary Length Units (Inches, Feet, And Yards)2Math2.MD.A.3Compare Fractions With The Same Numerator3Math3.NF.A.3dUnderstand Thousandths And Read And Write Decimals To Thousandths5Math5.NBT.A.3aMeasures Of Center: Mean, Median, And Mode6Math6.SP.A.2, 6.SP.A.3, 6.SP.B.5cUnderstand and Write Equivalent Expressions6Math6.EE.A.3, 6.EE.A.4View All WorksheetsRecommended Coloring PagesMoon buggy parked with an astronaut wavingPre-K – KAll SubjectsLowercase q with a small scepter leaning against itPre-K – KAll SubjectsPalm tree with coconuts and a small sun in the cornerPre-K – KAll SubjectsA family ice skating, each member wearing a winter scarf3 – 4All SubjectsFrustum at a playground with swings and a slide3 – 4All SubjectsCornish Rex Cat in a garden with flowers and butterflies3 – 4All SubjectsView All Coloring PagesRecommended BlogsDigital Citizenship Curriculum That Works for K-6 StudentsNovember 12, 2025Essential NGSS Lessons: 14 Research-Backed Resources for Elementary ScienceSeptember 29, 2025Best Science Websites for K-6 Classrooms: A Teacher's GuideSeptember 27, 2025Best School Unblockers: Essential Educational iPad Apps That Transform Learning for K-6 StudentsSeptember 18, 2025Digital Citizenship Curriculum: Essential Lessons for K-6 StudentsSeptember 17, 2025Making Financial Algebra Fun: How to Gamify Personal Finance for K-6 StudentsSeptember 17, 2025View All Blog PostsQUICK LINKSAbout UsPrivacy PolicyTerms of ServiceTOOLSHomework HelperGuide DesignerPodcast MakerPlan BuilderRESOURCESMath GlossaryEnglish GlossaryEnglish Language ArtsMathematicsScienceBook InsightsFun with WordsBlog© 2025 EDU.COM. All rights reserved.

智能索引记录