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Which of the following linear equation coincide with the line 4x + 5y = 15?
- a)8x + 10y = 25
- b)2x + 3y = 7
- c)7x + 14y = 17
- d)12x + 15y = 45
Correct answer is option 'D'. Can you explain this answer?
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Which of the following linear equation coincide with the line 4x + 5y ...
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Which of the following linear equation coincide with the line 4x + 5y ...
To determine which of the given linear equations coincides with the line 4x + 5y = 15, we need to compare the equations by rearranging them into the standard form (Ax + By = C) and checking if the coefficients A, B, and C are the same.
Given equation: 4x + 5y = 15
Let's rearrange the equation:
4x + 5y = 15
5y = -4x + 15
y = (-4/5)x + 3
Now, let's compare this equation with the given options:
a) 8x + 10y = 25
Comparing the coefficients, we see that A = 8, B = 10, and C = 25. These coefficients are not the same as in the given equation, so option a) does not coincide with the line.
b) 2x + 3y = 7
Comparing the coefficients, we see that A = 2, B = 3, and C = 7. These coefficients are not the same as in the given equation, so option b) does not coincide with the line.
c) 7x + 14y = 17
Comparing the coefficients, we see that A = 7, B = 14, and C = 17. These coefficients are not the same as in the given equation, so option c) does not coincide with the line.
d) 12x + 15y = 45
Comparing the coefficients, we see that A = 12, B = 15, and C = 45. These coefficients are the same as in the given equation, so option d) coincides with the line.
Therefore, the correct answer is option d) 12x + 15y = 45.
Given equation: 4x + 5y = 15
Let's rearrange the equation:
4x + 5y = 15
5y = -4x + 15
y = (-4/5)x + 3
Now, let's compare this equation with the given options:
a) 8x + 10y = 25
Comparing the coefficients, we see that A = 8, B = 10, and C = 25. These coefficients are not the same as in the given equation, so option a) does not coincide with the line.
b) 2x + 3y = 7
Comparing the coefficients, we see that A = 2, B = 3, and C = 7. These coefficients are not the same as in the given equation, so option b) does not coincide with the line.
c) 7x + 14y = 17
Comparing the coefficients, we see that A = 7, B = 14, and C = 17. These coefficients are not the same as in the given equation, so option c) does not coincide with the line.
d) 12x + 15y = 45
Comparing the coefficients, we see that A = 12, B = 15, and C = 45. These coefficients are the same as in the given equation, so option d) coincides with the line.
Therefore, the correct answer is option d) 12x + 15y = 45.
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