Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. 2, x, plus, y, equals, 3 2x y= 3 minus, 2, x, minus, y, equals, minus, 6 −2x−y= −6

Answer 1

The given system of equations has exactly one solution, which is x = -3/4 and y = 9/2.

Step-by-step explanation:

The given system of equations is:

2x + y = 3 ...(1)

2x - y = -6 ...(2)

To determine the type of solution, we can solve these equations using the method of elimination or substitution.

Add equations (1) and (2) to eliminate y:

(2x + y) + (2x - y) = 3 + (-6)

4x = -3

x = -3/4

Substitute this value of x into equation (1) to find y:

2(-3/4) + y = 3

-3/2 + y = 3

y = 9/2

Therefore, the system of equations has exactly one solution, which is x = -3/4 and y = 9/2.