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Graphically, the pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
Represents two lines which are:
- a)Intersecting at exactly one point
- b)Intersecting at exactly two points
- c)Coincident
- d)Parallel
Correct answer is option 'D'. Can you explain this answer?
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Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Repre...
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a1 / a2 = 6 / 2 = 3 / 1
b1 / b2 = -3 / -1 = 3 / 1
c1 / c2 = 10 / 9
This implies
a1 / a2 = b1 / b2 ≠ c1 / c2
Most Upvoted Answer
Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Repre...
Given equations:
Equation 1: 6x - 3y + 10 = 0
Equation 2: 2x - y + 9 = 0
Graphical representation:
To determine the graphical representation of the given equations, we need to convert them into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Converting Equation 1:
6x - 3y + 10 = 0
-3y = -6x - 10
y = 2x + (10/3)
Converting Equation 2:
2x - y + 9 = 0
-y = -2x - 9
y = 2x + 9
Explanation:
The slope-intercept form of Equation 1 is y = 2x + (10/3), which indicates that the slope of the line is 2. Similarly, the slope-intercept form of Equation 2 is y = 2x + 9, which also indicates a slope of 2.
Since the slopes of both lines are equal, but the y-intercepts are different, the lines are parallel. When two lines are parallel, they never intersect. Hence, the correct answer is option D, "Parallel".
Graphical representation:
To visually represent the lines on a graph, we can plot a few points and connect them to form the lines.
For Equation 1:
Let's assume x = 0, then y = (10/3) [point (0, 10/3)]
Let's assume x = 3, then y = 8 [point (3, 8)]
For Equation 2:
Let's assume x = 0, then y = 9 [point (0, 9)]
Let's assume x = 3, then y = 15 [point (3, 15)]
Plotting these points on a graph, we can see that the lines never intersect and run parallel to each other.
Equation 1: 6x - 3y + 10 = 0
Equation 2: 2x - y + 9 = 0
Graphical representation:
To determine the graphical representation of the given equations, we need to convert them into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Converting Equation 1:
6x - 3y + 10 = 0
-3y = -6x - 10
y = 2x + (10/3)
Converting Equation 2:
2x - y + 9 = 0
-y = -2x - 9
y = 2x + 9
Explanation:
The slope-intercept form of Equation 1 is y = 2x + (10/3), which indicates that the slope of the line is 2. Similarly, the slope-intercept form of Equation 2 is y = 2x + 9, which also indicates a slope of 2.
Since the slopes of both lines are equal, but the y-intercepts are different, the lines are parallel. When two lines are parallel, they never intersect. Hence, the correct answer is option D, "Parallel".
Graphical representation:
To visually represent the lines on a graph, we can plot a few points and connect them to form the lines.
For Equation 1:
Let's assume x = 0, then y = (10/3) [point (0, 10/3)]
Let's assume x = 3, then y = 8 [point (3, 8)]
For Equation 2:
Let's assume x = 0, then y = 9 [point (0, 9)]
Let's assume x = 3, then y = 15 [point (3, 15)]
Plotting these points on a graph, we can see that the lines never intersect and run parallel to each other.
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Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer?
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