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How many solutions are possible for the following pair of equations? x – y = 1 and 3x – 4y = 4
- a)No solution
- b)One
- c)Infinitely many solutions
- d)Two solutions
Correct answer is option 'B'. Can you explain this answer?
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How many solutions are possible for the following pair of equations?x ...
There are infinitely many solutions for the given pair of equations.
We can see this by first subtracting the second equation from the first:
x - 2y = 1 - 4y
Simplifying this, we get:
x = 1 - 2y
Substituting this value of x into the first equation, we get:
(1 - 2y)^2 + y^2 = 5
Expanding and simplifying this equation, we get:
5y^2 - 4y - 4 = 0
Using the quadratic formula, we can solve for y:
y = (4 ± √36)/10
y = (4 ± 6)/10
y = 1 or y = -0.4
Substituting these values of y back into the equation x = 1 - 2y, we get:
if y = 1, then x = -1
if y = -0.4, then x = 1.8
Therefore, there are infinitely many solutions for the given pair of equations, since any value of y can be chosen, and the corresponding value of x can be calculated using x = 1 - 2y.
We can see this by first subtracting the second equation from the first:
x - 2y = 1 - 4y
Simplifying this, we get:
x = 1 - 2y
Substituting this value of x into the first equation, we get:
(1 - 2y)^2 + y^2 = 5
Expanding and simplifying this equation, we get:
5y^2 - 4y - 4 = 0
Using the quadratic formula, we can solve for y:
y = (4 ± √36)/10
y = (4 ± 6)/10
y = 1 or y = -0.4
Substituting these values of y back into the equation x = 1 - 2y, we get:
if y = 1, then x = -1
if y = -0.4, then x = 1.8
Therefore, there are infinitely many solutions for the given pair of equations, since any value of y can be chosen, and the corresponding value of x can be calculated using x = 1 - 2y.
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How many solutions are possible for the following pair of equations?x ...
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