Question

Number graph ranging from negative one to seven on the x axis and negative four to four on the y axis. Two lines that are perpendicular to each other intersect at (two, one). The line with a positive slope is labeled a and the line with a negative slope is labeled b. Use the graph to state the solution for the system. x + 2y = 4 (line a) 3x – 2y = 4 (line b) (2, –1) (2, –1) (2, 1) (2, 1) (–2, 1)

Answer 1

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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