Question

1. Solve the system.

y= 1/7x-4
x= 7y+1

A. There are an infinite number of solutions.
B. (–13, –2)
C. (7, –3)
D. No solution

Answer 1

D

Explanation:

We put 2nd equation into 1st equation and get y:

`y=(1)/(7)x-4\\y=(1)/(7)(7y+1)-4\\y=y+(1)/(7)-4\\y=y-(15)/(4)\\NOTHING`

We can't seem to come to a solution.

Also let's rearrange the 2nd equation into y = something form:

x = 7y + 1

7y = x - 1

y = 1/7 x -1

As we can see BOTH the lines have the same SLOPE, the number before x, which is 1/7 and we know that lines with same slope are parallel, they never intersect.

Having a solution to a system means their intersection point, since they are parallel lines, they don't intersect, and hence DO NOT HAVE A SOLUTION.

D is the correct choice.