Drag each pair of equations to show if the system has no solutions, one solution, or infinitely many solutions.

Remark

Please number your pairs of equations going from left to right. The pair on the extreme left is (1) and the pair on the extreme right is (5).

(1)

If you multiply to top member of the pair by 2, you will get the bottom equation of the pair. What that tells you is that there are many (infinite) numbers of solutions.

(y = 3x + 4) * 2 remove the brackets.

2y = 6x + 8 Exactly the same equation as the bottom one = infinite solutions.

(2)

If the slopes are the same (both are -1) and the y intercepts are different (0,-2) and (0,-6) then the lines are parallel (they never meet) and have no solutions.

(3)

If the slopes are different, there is one solution. (9 and 1) There is one solution.

(4)

Four gives 1 solution as well at 0,0. That is because the slopes are different.

(5)

trick question. the slopes are quite different. one is 0 and the other is undefined. They meet at one point.(-6,-3). I solution.

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

step-by-step explanation: