If (x+3y=19) and (2x-y=3), what is the value of (x+2y)?
Answer and explanation
Correct answer: 14
From the second equation, 2x-y=3, solve for y to obtain y=2x-3. Substitute this into x+3y=19: x+3(2x-3)=19. Simplifying gives x+6x-9=19, so 7x=28 and x=4. Then y=2(4)-3=5. The required expression is x+2y=4+2(5)=14, so option D is correct. Verification in the original equations gives 4+15=19 and 8-5=3. The distractors 11, 12, and 13 may result from using only one variable, subtracting instead of adding the final terms, or making an arithmetic error, but none equals the correctly evaluated expression. The governing idea is to solve the pair first, then substitute the ordered values into the requested expression rather than confusing it with either original equation.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
From the second equation, 2x-y=3, solve for y to obtain y=2x-3. Substitute this into x+3y=19: x+3(2x-3)=19. Simplifying gives x+6x-9=19, so 7x=28 and x=4. Then y=2(4)-3=5. The required expression is x+2y=4+2(5)=14, so option D is correct. Verification in the original equations gives 4+15=19 and 8-5=3. The distractors 11, 12, and 13 may result from using only one variable, subtracting instead of adding the final terms, or making an arithmetic error, but none equals the correctly evaluated expression. The governing idea is to solve the pair first, then substitute the ordered values into the requested expression rather than confusing it with either original equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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