Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Easy
0 reads0 ratings0 helpful

What is the value of x from 5x + y = 31 and 3x + y = 19?

Answer and explanation

Correct answer: x = 6

The governing concept is elimination of a common variable. Since y has the same coefficient, +1, in both equations, subtract the second equation from the first: (5x + y) − (3x + y) = 31 − 19. The y terms cancel, leaving 2x = 12. Dividing by 2 gives x = 6, so option A is correct. Verification confirms the result: substituting x = 6 into 3x + y = 19 gives 18 + y = 19 and hence y = 1. The first equation then gives 5(6) + 1 = 30 + 1 = 31. Therefore both equations are satisfied. The other proposed values 5, 4, and 3 do not make the difference of the left sides equal to 12 and cannot be the common solution.

Related tags

Linear EquationsElimination MethodValue Of XClass 10Algebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two VariablesMathematics
सुधार सुझाएँ / Earn

Was this question useful?

No ratings yetWrite a review / Rate this question

Student Reviews

No published reviews yet.

KEEP PRACTISING

10 more MCQs
  1. 1In the equation \(2x-y=4\), what is the value of \(y\) when \(x=3\)?
  2. 2Which equation is obtained by simplifying (6x+3y=12)?
  3. 3What is the point of intersection of the lines \(4x+3y=34\) and \(4x-y=10\)?
  4. 4If the lines \(x+y=9\) and \(kx+3y=23\) both pass through the point \(\left(4,5\right)\), what is the value of \(k\)?
  5. 5While solving a pair of linear equations in two variables by the elimination method, in which situation can one variable be eliminated directly?
  6. 6What is the \(x\)-coordinate of the point of intersection of the lines \(4x+5y=31\) and \(3x-2y=1\)?
  7. 7If the two lines have a unique point of intersection (r, s) that satisfies 3r + s = 19 and r − s = 1, what is the value of r + s?
  8. 8The unique point of intersection of two lines is (r, s). If the lines are represented by 4r + s = 29 and r − s = 1, what is the value of r + s?
  9. 9What is the solution of the equations (x+y=5) and (x-y=1)?
  10. 10In the equations (2x+y=7) and (x=2), what is the value of (y)?
Found an issue? Help improve this questionMy reports and replies

Add Muft Shiksha to your Home Screen

In Safari, tap Share, then Add to Home Screen.