Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
2, x, plus, y, equals, minus, 3
2x+y=
−3
minus, 2, x, minus, y, equals, 5
−2x−y=
5

Answer 1

To determine the number of solutions for the given system of equations, we can solve it using elimination or substitution.

Using elimination:
To eliminate the variable "y," we can multiply the second equation by -1 and add it to the first equation:
2x + y = -3
-(-2x - y = 5)
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4x = 2
Dividing both sides of the equation by 4, we get:
x = 1/2

Now, we can substitute the value of x into one of the equations to solve for y:
2(1/2) + y = -3
1 + y = -3
y = -4

Therefore, the system of equations has exactly one solution: x = 1/2 and y = -4.

Thus, the correct answer is: exactly one solution.