To find the solution to the system of equations represented by the two lines, we first need to determine the equations of both lines from the given points.
Line 1: It passes through the points (0, -5) and (-5, 0).
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Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-5)}{-5 - 0} = \frac{5}{-5} = -1 \]
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Use the slope-intercept form \(y = mx + b\). Since one point (0, -5) is the y-intercept (b), we have: \[ y = -1x - 5 \] or simplified: \[ y = -x - 5 \]
Line 2: It passes through the points (0, -5) and (-2, 1).
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Calculate the slope (m): \[ m = \frac{1 - (-5)}{-2 - 0} = \frac{6}{-2} = -3 \]
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Again use the slope-intercept form \(y = mx + b\). Using point (0, -5) as the y-intercept: \[ y = -3x - 5 \]
Now we have the two equations:
- \(y = -x - 5\) (Line 1)
- \(y = -3x - 5\) (Line 2)
Next, we will set these two equations equal to find the intersection point:
\[ -x - 5 = -3x - 5 \]
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Add \(3x\) to both sides: \[ 2x - 5 = -5 \]
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Add 5 to both sides: \[ 2x = 0 \]
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Divide by 2: \[ x = 0 \]
Substituting \(x = 0\) back into one of the original equations to find \(y\): Using \(y = -x - 5\): \[ y = -0 - 5 = -5 \]
Thus, the solution to the system of equations is the point \((0, -5)\).
Looking at the provided answer choices, the correct answer is: \[ \boxed{(0, -5)} \]
1 answer