Question
Download Solution PDFThe point of intersection of the graphs of the equations 147x - 231y = 525 and 77x - 49y = 203, lies on the graph on the equation:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
147x - 231y = 525
77x - 49y = 203
Formula used:
To find the intersection point, solve the system of equations.
Calculation:
Multiply the second equation by 3:
⇒ 231x - 147y = 609
Now subtract the first equation from the modified second equation:
⇒ (231x - 147y) - (147x - 231y) = 609 - 525
⇒ 84x + 84y = 84
⇒ x + y = 1
Using x + y = 1 in the first equation:
⇒ 147x - 231(1 - x) = 525
⇒ 147x - 231 + 231x = 525
⇒ 378x = 756
⇒ x = 2
Using x = 2 in x + y = 1:
⇒ 2 + y = 1
⇒ y = -1
So, the intersection point is (2, -1).
Now check which equation the point (2, -1) satisfies:
For 9x - 5y = 23:
⇒ 9(2) - 5(-1) = 18 + 5 = 23
∴ The correct answer is option 1.
Last updated on Dec 9, 2024
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