The pairs of equations x + 2y - 5 = 0 and -4x - 8y + 20 = 0 have:a)Un...
A
1 / a
2 = 1 / -4
b1 / b2 = 2 / -8 = 1 / -4
c1 / c2 = -5 / 20 = -1 / 4
This shows:
a1 / a2 = b1 / b2 = c1 / c2
Therefore, the pair of equations has infinitely many solutions.
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The pairs of equations x + 2y - 5 = 0 and -4x - 8y + 20 = 0 have:a)Un...
Solution:
Given equations are x - 2y = 5 and -4x - 8y + 20 = 0.
To find the number of solutions, we can solve the equations by using any of the methods like substitution, elimination or cross-multiplication.
Method 1: Substitution Method
From the first equation, we get x = 2y + 5.
Substituting this value of x in the second equation, we get:
-4(2y + 5) - 8y + 20 = 0
-8y - 20 - 8y + 20 = 0
-16y = 0
y = 0
Substituting this value of y in the first equation, we get:
x - 2(0) = 5
x = 5
Hence, the solution of the given system of equations is (x, y) = (5, 0).
Method 2: Elimination Method
Multiplying the first equation by 4, we get:
4x - 8y = 20
Adding this equation to the second equation, we get:
4x - 8y - 4x - 8y + 20 = 0
-16y + 20 = 0
y = 5/4
Substituting this value of y in the first equation, we get:
x - 2(5/4) = 5
x = 15/4
Hence, the solution of the given system of equations is (x, y) = (15/4, 5/4).
Conclusion:
Since we have obtained two different solutions for the given system of equations, it implies that the equations have infinitely many solutions.
Therefore, the correct option is (C) - Infinitely many solutions.
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