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The system of linear equations
4x + 2y = 7
2x + y = 6 has
4x + 2y = 7
2x + y = 6 has
- a)A unique solution
- b)no solution
- c)An infinite number of solutions
- d)exactly two distinct solutions
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The system of linear equations4x + 2y = 72x + y = 6 hasa)A uniqu...
(b) This can be written as AX = B Where A
Angemented matrix
rank(A) ≠ rank(
). The system is inconsistant .So system has no solution.
). The system is inconsistant .So system has no solution.Most Upvoted Answer
The system of linear equations4x + 2y = 72x + y = 6 hasa)A uniqu...
Solution:
To determine the number of solutions, we can use the method of elimination or substitution. Here, we will use the method of elimination.
Multiplying the second equation by 2, we get:
4x + 2y = 7 (Equation 1)
4x + 2y = 12 (Equation 2)
Subtracting Equation 1 from Equation 2, we get:
0 = 5
This is a contradiction, which means that the system has no solution.
Explanation:
In this system of equations, we have two variables (x and y) and two equations. The solution to the system is the values of x and y that satisfy both equations simultaneously.
If the two equations represent two lines that intersect at a single point, then the system has a unique solution. If the two equations represent two parallel lines, then the system has no solution. If the two equations represent the same line, then the system has an infinite number of solutions.
In this case, we can rewrite the two equations in slope-intercept form:
4x + 2y = 7
2y = -4x + 7
y = -2x + 7/2
2x + y = 6
y = -2x + 6
Both equations have the same slope (-2), but different y-intercepts (7/2 and 6). Therefore, the two lines are parallel and never intersect. This means that there is no solution to the system of equations.
Therefore, the correct answer is option B: no solution.
To determine the number of solutions, we can use the method of elimination or substitution. Here, we will use the method of elimination.
Multiplying the second equation by 2, we get:
4x + 2y = 7 (Equation 1)
4x + 2y = 12 (Equation 2)
Subtracting Equation 1 from Equation 2, we get:
0 = 5
This is a contradiction, which means that the system has no solution.
Explanation:
In this system of equations, we have two variables (x and y) and two equations. The solution to the system is the values of x and y that satisfy both equations simultaneously.
If the two equations represent two lines that intersect at a single point, then the system has a unique solution. If the two equations represent two parallel lines, then the system has no solution. If the two equations represent the same line, then the system has an infinite number of solutions.
In this case, we can rewrite the two equations in slope-intercept form:
4x + 2y = 7
2y = -4x + 7
y = -2x + 7/2
2x + y = 6
y = -2x + 6
Both equations have the same slope (-2), but different y-intercepts (7/2 and 6). Therefore, the two lines are parallel and never intersect. This means that there is no solution to the system of equations.
Therefore, the correct answer is option B: no solution.
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Community Answer
The system of linear equations4x + 2y = 72x + y = 6 hasa)A uniqu...
X = 1 &
y = 1
y = 1
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