What is the y-coordinate of the intersection of 3x + 4y = 25 and 5x − 2y = 7?
Answer and explanation
Correct answer: 4
The governing concept is that the intersection coordinates satisfy both equations. Solve the pair by elimination. Multiply the second equation by 2: 10x − 4y = 14. Add this to the first equation, 3x + 4y = 25, to obtain 13x = 39, so x = 3. Substitute x = 3 into 5x − 2y = 7: 15 − 2y = 7, hence −2y = −8 and y = 4. Therefore the y-coordinate is 4, making option C correct. The other choices can result from reading the x-coordinate as the requested value, using only one equation incorrectly, or making an arithmetic error during elimination. Substitution into both original equations confirms the point (3, 4).
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is that the intersection coordinates satisfy both equations. Solve the pair by elimination. Multiply the second equation by 2: 10x − 4y = 14. Add this to the first equation, 3x + 4y = 25, to obtain 13x = 39, so x = 3. Substitute x = 3 into 5x − 2y = 7: 15 − 2y = 7, hence −2y = −8 and y = 4. Therefore the y-coordinate is 4, making option C correct. The other choices can result from reading the x-coordinate as the requested value, using only one equation incorrectly, or making an arithmetic error during elimination. Substitution into both original equations confirms the point (3, 4).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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