How many solutions does the following system have
{(x+y=3),(2x+2y=5):}
infinitely many solutions
one solution
no solutions
two solutions
no solutions
To determine the number of solutions of the given system of equations, we can solve them simultaneously.
The given system of equations is:
1) x + y = 3
2) 2x + 2y = 5
We can simplify equation 2 by dividing both sides by 2:
2x/2 + 2y/2 = 5/2
x + y = 5/2
Now we have two equations:
1) x + y = 3
2) x + y = 5/2
By comparing the two equations, we can see that they are parallel lines, as they have the same slope (1) and different y-intercepts (3 and 5/2).
Since the lines are parallel and never intersect, there are no solutions to this system of equations.
Therefore, the correct answer is: no solutions.