Question

y = -x - 2 y + 2 = -x Graph each system. Tell whether the system hasA.no solutionB.one solutionC. infinitely many solutionsD. Cannot determine

Answer 1

To graph each equation in the system, you can give it x-values, plug into the equations, and get values for Y.

Since a single line passes through two points, just take two values of x for each equation. So, for the first you have for example

*If x = 3

`\begin{gathered} y=-x-2 \\ y=-3-2 \\ y=-5 \\ \text{ So} \\ (3,-5) \end{gathered}`

*If x = -4

`\begin{gathered} y=-x-2 \\ y=-(-4)-2 \\ y=4-2 \\ y=2 \\ \text{ So,} \\ (-4,2) \end{gathered}`

For the second equation you have for example

*If x = 1

`\begin{gathered} y+2=-x \\ y+2=-1 \\ y+2-2=-1-2 \\ y=-3 \\ \text{ So,} \\ (1,-3) \end{gathered}`

*if x = -1

`\begin{gathered} y+2=-(-1) \\ y+2=1 \\ y+2-2=1-2 \\ y=-1 \\ \text{ So,} \\ (-1,-1) \end{gathered}`

Now, graphing the equations you have

As you can see, the lines associated with this system of equations overlap, that is, they share infinite solution points.

Therfore, the correct answer is C. infinitely many solutions.