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

There are infinitely many solutions.

Explanation:

The equation is $-\frac{1}{2} x+\frac{1}{2}y=-1$ and $x-y=2$

Now, we shall solve the equation by substitution method.

Let us substitute $x=y+2$ in $-\frac{1}{2} x+\frac{1}{2}y=-1$

$-\frac{1}{2}(y+2)+\frac{1}{2} y=-1$

Multiplying the terms within the bracket,

$-\frac{1}{2} y-1+\frac{1}{2} y=-1$

Adding both sides by 1, we get,

$-\frac{1}{2} y+\frac{1}{2} y=0$

Adding both sides by $\frac{1}{2} y$,

$\frac{1}{2} y=\frac{1}{2} y$

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

Answer 2

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 :))