Determine whether the point (2, 0) is a solution to the system of equations. Explain your reasoning in complete sentences.

Question

sohailiftikhar · Answer

just put these point in the place of variable and if they satisfy the equeation then they are solution sets ......

anonymous · Answer

how do I know if they satisfy them? I plugged it in and i got g(x) = 8 and f(x) = 2

anonymous · Answer

attachment

anonymous · Answer

That is a picture of the graph they gave us

sohailiftikhar · Answer

where tow lines will cut each other i will be the solution set of equeations...

anonymous · Answer

Oh okay so it should be (0,2) ?

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

If you have a graph showing all of the equations, any solution to all of the equations will be a point at which all of the equations intersect.  Is (2,0) such a point?

whpalmer4 · Answer

For the same value of $x$, both $f(x)$ and $g(x)$ must be equal for that value of $x$ to be a solution.

anonymous · Answer

Oh so I just plug in 2 for x in both of my solutions and 0 for y?

whpalmer4 · Answer

$$y = f(x) = |x-1|+1$$$$y = g(x) = 3x+2$$If we think $x=2$ might be a solution, then
$$f(2) = g(2)$$but $$f(2) = |2-1|+1 = 2$$and $$g(2) = 3(2) +2 = 8$$ and those are not equal...

whpalmer4 · Answer

Yes, you could also do it that way as a check:

$$0 = f(2) = |2-1|+1\checkmark$$so far, so good, but let's try the other equation, which also must work:
$$0 = g(2) = 3(2)+2 = 8$$Bzzt, wrong!
So $(2,0$ is NOT a solution to that system of equations.

whpalmer4 · Answer

sorry, $(2,0)$ is not a solution

anonymous · Answer

Okay thats what I thought. Thank you.