Question

Consider the following system of equations: y = 5x + 6 y = −x − 7 Which description best describes the solution to the system of equations?
Line y = 5x + 6 intersects line y = −x − 7.
Lines y = 5x + 6 and y = −x − 7 intersect the x-axis.
Lines y = 5x + 6 and y = −x − 7 intersect the y-axis.
Line y = 5x + 6 intersects the origin.

Answer 1

Answer:

The answer is A. Line y = 5x + 6 intersects line y = −x − 7.

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Answer 2

 y = 5x + 6
y = −x − 7 

5x + 6 = -x - 7
6x + 6 = -7
6x = -13
x = -13/6

y = 5(-13/6) + 6
y = -29/6

The solution is (-13/6, -29/6) and that tells us that the two ines do not intersect at the origin or any of the two axis. If they intersected at the origin, then the solution should have been (0, 0). If they intersected at the x-axis, the solution should have been (x, 0). If the two lines intersected at the y-axis, the solution would have been (0, y).

The answer is A) Line y = 5x + 6 intersects line y = −x − 7.