If a is an integer, prove that (14a + 3, 21a + 4) = 1.
1 answer:
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Answer:
The solutions are:
(-15 , -4) ⇒ 1st
(3 , 2) ⇒ 3rd
(21 , 8) ⇒ 5th
Step-by-step explanation:
To find the solution of the graph let us make the equation of the line by using any two points on the line
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
The formula of the slope is
From the figure
∵ The line passes through points (-3 , 0) and (0 , 1)
- Find the slope of the line
∴
- Substitute the value of m in the form of the equation
∴ y = x + b
∵ b is the value of y at x = 0
∵ y = 1 at x = 0 ⇒ y-intercept
∴ b = 1
∴ y = x + 1
Lets substitute the x-coordinate of each point to find the y-coordinate, if the y-coordinate is equal to the y-coordinate of the points, then the point is a solution
Point (-15 , -4)
∵ x = -15
∴ y = (-15) + 1
∴ y = -5 + 1 = -4 ⇒ same value of the point
∴ (-15 , -4) is a solution
Point (-6 , 1)
∵ x = -6
∴ y = (-6) + 1
∴ y = -2 + 1 = -1 ⇒ not the same value of the point
∴ (-6 , 1) is not a solution
Point (3 , 2)
∵ x = 3
∴ y = (3) + 1
∴ y = 1 + 1 = 2 ⇒ same value of the point
∴ (3 , 2) is a solution
Point (12 , 9)
∵ x = 12
∴ y = (12) + 1
∴ y = 4 + 1 = 5 ⇒ not the same value of the point
∴ (12 , 9) is not a solution
Point (21 , 8)
∵ x = 21
∴ y = (21) + 1
∴ y = 7 + 1 = 8 ⇒ same value of the point
∴ (21 , 8) is a solution