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The pairs of equations x + 2y - 5 = 0 and -4x - 8y + 20 = 0 have:
- a)Unique solution
- b)Exactly two solutions
- c)Infinitely many solutions
- d)No solution
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The pairs of equations x + 2y - 5 = 0 and -4x - 8y + 20 = 0 have:a)Uni...
a1/a2 = 1/-4
b1/b2 = 2/-8 = 1/-4
c1/c2 = -5/20 = -¼
This shows:
a1/a2 = b1/b2 = c1/c2
Therefore, the pair of equations has infinitely many solutions.
b1/b2 = 2/-8 = 1/-4
c1/c2 = -5/20 = -¼
This shows:
a1/a2 = b1/b2 = c1/c2
Therefore, the pair of equations has infinitely many solutions.
Most Upvoted Answer
The pairs of equations x + 2y - 5 = 0 and -4x - 8y + 20 = 0 have:a)Uni...
To determine the number of solutions for the given pair of equations, we need to solve the equations simultaneously and analyze the nature of their solution.
Given equations:
1) x + 2y - 5 = 0
2) -4x - 8y + 20 = 0
To solve these equations, we can use the method of substitution or elimination.
Using the method of substitution:
1) Rearrange equation 1 to express x in terms of y:
x = 5 - 2y
2) Substitute x in equation 2 with the value obtained in step 1:
-4(5 - 2y) - 8y + 20 = 0
-20 + 8y - 8y + 20 = 0
0 = 0
The equation 0 = 0 indicates that the equation is always true, regardless of the value of y. This suggests that the two equations represent the same line and have infinitely many solutions.
Using the method of elimination:
1) Multiply equation 1 by -4 to make the coefficients of x in both equations equal:
-4x - 8y + 20 = 0
2) Adding equation 1 and equation 2:
x + 2y - 5 + (-4x - 8y + 20) = 0
-3x + 12 = 0
-3x = -12
x = 4
3) Substitute the value of x in equation 1:
4 + 2y - 5 = 0
2y - 1 = 0
2y = 1
y = 1/2
The solution to the system of equations is (x, y) = (4, 1/2). This represents a unique solution.
Therefore, the correct answer is option 'C' - Infinitely many solutions.
Given equations:
1) x + 2y - 5 = 0
2) -4x - 8y + 20 = 0
To solve these equations, we can use the method of substitution or elimination.
Using the method of substitution:
1) Rearrange equation 1 to express x in terms of y:
x = 5 - 2y
2) Substitute x in equation 2 with the value obtained in step 1:
-4(5 - 2y) - 8y + 20 = 0
-20 + 8y - 8y + 20 = 0
0 = 0
The equation 0 = 0 indicates that the equation is always true, regardless of the value of y. This suggests that the two equations represent the same line and have infinitely many solutions.
Using the method of elimination:
1) Multiply equation 1 by -4 to make the coefficients of x in both equations equal:
-4x - 8y + 20 = 0
2) Adding equation 1 and equation 2:
x + 2y - 5 + (-4x - 8y + 20) = 0
-3x + 12 = 0
-3x = -12
x = 4
3) Substitute the value of x in equation 1:
4 + 2y - 5 = 0
2y - 1 = 0
2y = 1
y = 1/2
The solution to the system of equations is (x, y) = (4, 1/2). This represents a unique solution.
Therefore, the correct answer is option 'C' - Infinitely many solutions.
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