Tell whether the ordered pair (?4,?2) is a solution of the system of linear equations. Y=2x+6 y=-3x-14
1 answer:
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Answer:
The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2) ⇒ D
Step-by-step explanation:
<em>To solve this type of question, Form the equation of the line and substitute the x-coordinate of each ordered pair to find y, if the value of y equal to the value of the y-coordinate of the point, then the point is on the line</em>
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 rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m =
From the given figure
∵ The line passes through points (-4, 0) and (0, 4)
∴ x1 = -4 and y1 = 0
∴ x2 = 0 and y2 = 4
→ Substitute them in the rule above
∵ m = =
=
∴ m = 1
∵ b is the value of y at x = 0
∵ y = 4 at x = 0
∴ b = 4
→ Substitute the values of m and b in the form of the equation above
∴ y = 1(x) + 4
∴ y = x + 4 ⇒ equation of the given line
Let us check every group
∵ The ordered pairs are (7, 3), (6, 2), (2, -2)
∵ y = x + 4
∵ x = 7
∵ y = 7 + 4 = 11
∵ y-coordinate = 3
∴ Point (7, 3) doesn't lie on the line
∵ The ordered pairs are (5, 1), (3, 7), (2, 6)
∵ x = 5
∴ y = 5 + 4 = 9
∵ y-coordinate = 1
∴ Point (5, 1) doesn't lie on the line
∵ The ordered pairs are (3, 7), (2, 6), (2, 2)
∵ x = 3
∴ y = 3 + 4 = 7
∵ y-coordinate = 7
∴ Point (3, 7) lies on the line
∵ x = 2
∴ y = 2 + 4 = 6
∵ y-coordinate = 6
∴ Point (2, 6) lies on the line
∵ x = 2
∴ y = 6
∵ y-coordinate = 2
∴ Point (2, 2) doesn't lie on the line
∵ The ordered pairs are (3, 7), (2, 6), (-2, 2)
∵ x = 3
∴ y = 3 + 4 = 7
∵ y-coordinate = 7
∴ Point (3, 7) lies on the line
∵ x = 2
∴ y = 2 + 4 = 6
∵ y-coordinate = 6
∴ Point (2, 6) lies on the line
∵ x = -2
∴ y = -2 + 4 = 2
∵ y-coordinate = 2
∴ Point (-2, 2) lies on the line
∵ The three ordered pairs lie on the line
∴ The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2)
∵ The ordered pairs are (1, 5), (-6, 2), (-7, -3)
∵ x = 1
∴ y = 1 + 4 = 5
∵ y-coordinate = 5
∴ Point (1, 5) lies on the line
∵ x = -6
∴ y = -6 + 4 = -2
∵ y-coordinate = 2
∴ Point (-6, 2) doesn't lie on the line