To find the solution to the system of linear equations represented by the two intersecting lines on the graph, you need to find the coordinates of the intersection point of the two lines.
Since you mentioned that the y-intercept is (0, 2), we know that one of the lines crosses the y-axis at this point. The other points given are (1, 4) and (6, 2); however, we need to check if these points lie on the same line or different lines.
By examining the given points, we can potentially derive the equations of both lines.
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Using the points (0, 2) and (1, 4) to derive the first line's equation:
- Slope (m) = (y2 - y1) / (x2 - x1) = (4 - 2) / (1 - 0) = 2
- The equation can be written in slope-intercept form: \( y = mx + b \)
- So, it becomes \( y = 2x + 2 \).
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Using the points (0, 2) and (6, 2) to derive the second line's equation:
- Since the y-coordinate is constant at 2 for the second line, that line is horizontal: \( y = 2 \).
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Finding the intersection:
- Set the equations equal to each other to find the intersection point: \[ 2 = 2x + 2 \]
- Solving for x: \[ 2x = 0 \implies x = 0 \]
- Now substitute \( x = 0 \) into \( y = 2 \): \[ y = 2 \]
The intersection point, which is the solution to the system of equations, is (0, 2).
Thus, the ordered pair is:
\[ \text{(0, 2)} \]
In coordinate boxes, you would enter:
\[ (0, 2) \]
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