Asked by haechan
Determine the number of solutions of this system of linear equations:%0D%0A%0D%0A−x+y=3%0D%0A−%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A3%0D%0A %0D%0A%0D%0A−2x+2y=3
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Answered by
GPT 3.5
To determine the number of solutions, we need to check if the two lines represented by these equations are parallel, coincident, or intersecting.
The given system of equations is:
1. −x + y = 3
2. −2x + 2y = 3
Let's rewrite equation 2 by dividing both sides by 2:
2'. -x + y = 1.5
Comparing equations 1 and 2', it can be seen that the two equations are different but they also have a proportional relationship. This means they represent parallel lines and do not intersect.
Therefore, this system of equations has no solutions.
The given system of equations is:
1. −x + y = 3
2. −2x + 2y = 3
Let's rewrite equation 2 by dividing both sides by 2:
2'. -x + y = 1.5
Comparing equations 1 and 2', it can be seen that the two equations are different but they also have a proportional relationship. This means they represent parallel lines and do not intersect.
Therefore, this system of equations has no solutions.
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