The solution for the system of lines is defined as follows,
x-Intercept for line a: (4,0)
y-Intercept for line a: (0,2)
x-Intercept for line b: (1.5, -0)
y-Intercept for line b: (0,-2)
Line a and b intersect at (2,1)
Solving the System of Lines:
Line a: x + 2y = 4
Line b: 3x – 2y = 4
From the graph,
Line a intersect x-axis at (4,0) and y-axis at (0,2)
Line b intersect x-axis at (-1.5,0) and y-axis at (0,-2)
x + 2y = 4
x = 4-2y
Since point P lies on bot the lines A and B, it will satisfy the equations of both a and b.
Thus, substituting x = 4-2y in the equation of line b, we get,
3(4-2y) - 2y = 4
12 - 6y - 2y = 4
8y = 8
y = 1
Putting y=1 in the equation of line a, x = 4-2y, we get,
x = 4-2(1)
x = 4-2
x = 2
Hence, point P≡(2,1).
Learn more about a line here:
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