Question

What is the solution to the system of equations? Negative one-half x + one-half y = negative 1 x minus y = 2 There is no solution. There are infinitely many solutions. There is only one solution, (3, 1). There is only one solution, (–6, –8).

Answer 1

I know I'm like 2 years late but the answer is B, for the future people that gets this question for the unit test..I got it right on edge. 2022.

Have a great day :))

Answer 2

There are infinitely many solutions.

Step-by-step explanation:

The equation is
`-(1)/(2) x+(1)/(2)y=-1` and
`x-y=2`

Now, we shall solve the equation by substitution method.

Let us substitute
`x=y+2` in
`-(1)/(2) x+(1)/(2)y=-1`

`-(1)/(2)(y+2)+(1)/(2) y=-1`

Multiplying the terms within the bracket,

`-(1)/(2) y-1+(1)/(2) y=-1`

Adding both sides by 1, we get,

`-(1)/(2) y+(1)/(2) y=0`

Adding both sides by
`(1)/(2) y`,

`(1)/(2) y=(1)/(2) y`

Since, both sides of the equation are equal, the system of equations have infinitely many solutions.