According to the graph, what is the solution (ordered pair) of this system of equations?​

Answers:

(2, -3) and (3, -3)

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Work Shown:

Since f(x) = -3, we'll replace f(x) with -3 and solve for x

f(x) = x^2 - 5x + 3

-3 = x^2 - 5x + 3 .... f(x) replaced with -3

0 = x^2 - 5x + 3 + 3 ... adding 3 to both sides

0 = x^2 - 5x + 6

x^2 - 5x + 6 = 0

(x - 3)(x - 2) = 0 .... factor; you can also apply the quadratic formula

x = 3 or x = 2

So that explains where that '2' comes from when they listed (2, ?)

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To find what replaces the question mark, we will plug x = 2 into the function

f(x) = x^2 - 5x + 3

f(2) = 2^2 - 5(2) + 3

f(2) = 4 - 10 + 3

f(2) = -3

We could have skipped this portion and said that the solution is (2,-3) but plugging x = 2 into the function to get the output y = -3 helps confirm that x = 2 is one of the x solutions.

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Let's do the same for x = 3

f(x) = x^2 - 5x + 3

f(3) = 3^2 - 5(3) + 3

f(3) = 9 - 15 + 3

f(3) = -3

We end up with the same output, so x = 3 is confirmed as well.

The graph below visually helps reinforce these confirmations. Each solution  is an intersection between the two curves.

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves