For what value of a would the following system of equations have infinitely many solutions?x - 2y = 153x - 6y = 5a
Question
For what value of a would the following system of equations have infinitely many solutions?x - 2y = 153x - 6y = 5a
Solution
The system of equations given is:
- x - 2y = 15
- 3x - 6y = 5a
To find the value of 'a' for which the system of equations has infinitely many solutions, the two equations must be equivalent to each other. This means that the second equation must be a multiple of the first.
First, let's express the second equation in terms of the first:
If we multiply the first equation by 3, we get:
3x - 6y = 45
Now, for the system to have infinitely many solutions, the right side of this equation should be equal to the right side of the second equation. So, we set them equal to each other:
45 = 5a
Now, solve for 'a':
a = 45 / 5 a = 9
So, the system of equations has infinitely many solutions when a = 9.
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