Question

Which TWO systems of equations have exactly one solution ?

6x−3y=3
2x−y=4



y=−2x−8
y=x+1



6x−3y=12
2x−y=4



x−4y=8
3x+2y=10



y=2x+1
y=2x−2

Answer 1

Answer: 2nd and 4th set

Explanation:

1st set has no solution because the left side of the second equation is that of the first equation divided by 3, but the right side is not.

2nd set has 1 solution because it is the set of 2 lines with different slopes and y-intercepts.

3rd set has infinitely many solutions because multiplying the top equation by 1/3 gives you the bottom equation.

4th set has only solution for the same reason as 2nd set.

5th set has no solution because the two lines are parallel, but have different y intercepts, meaning they never intersect.