To find the solution to the system of linear functions represented by the two tables, we first need to determine the equations of the two linear functions.
Let's start with the first table:
| x | y | |----|----| | -4 | 26 | | -2 | 18 | | 0 | 10 | | 2 | 2 |
To find the slope (m) of the first function, we can use two points. Let's take the points (0, 10) and (2, 2):
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Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 10}{2 - 0} = \frac{-8}{2} = -4 \]
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Use point-slope form to find the equation. Using point (0, 10): \[ y - 10 = -4(x - 0) \implies y = -4x + 10 \]
The first function is \( y = -4x + 10 \).
Next, let's examine the second table:
| x | y | |----|----| | -4 | 14 | | -2 | 8 | | 0 | 2 | | 2 | -4 |
Again, calculate the slope (m) using points (0, 2) and (2, -4):
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Calculate the slope (m): \[ m = \frac{-4 - 2}{2 - 0} = \frac{-6}{2} = -3 \]
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Use point-slope form to find the equation. Using point (0, 2): \[ y - 2 = -3(x - 0) \implies y = -3x + 2 \]
The second function is \( y = -3x + 2 \).
Now we have the system of equations:
- \( y = -4x + 10 \)
- \( y = -3x + 2 \)
To find the solution, set the equations equal to each other: \[ -4x + 10 = -3x + 2 \]
Solving for x: \[ -4x + 3x = 2 - 10 \ -x = -8 \ x = 8 \]
Now, substitute \( x = 8 \) into either equation to find y. Using the second equation: \[ y = -3(8) + 2 = -24 + 2 = -22 \]
The solution to the system is: \[ (8, -22) \]
So, the answer is \( (8, -22) \).
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