Question 737325: How many solutions are there to this: y=-8x-37, x+3y=4
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! The quick answer is one (1) solution.
What you have is two straight lines and since they have different slopes, they are not parallel, thus will cross at one and only one point. That crossing point is called the solution to the system of equations. It is a unique point, no other point will satisfy the equality of BOTH equations. You don't ask for the solution, but I'll show you how to get it anyway.
Given:
(1) y = -8x - 37 and
(2) x + 3y = 4 or
(3) y = -(1/3)x + 4/3
Since y = y, set (1) = (3) yielding
(4) -8x - 37 = -(1/3)x + 4/3 or
(5) -3*8x - 3*37 = -x + 4 or
(6) -24x + x = 3*37 + 4 or
(7) -23x = 111 + 4 or
(8) -23x = 115 or
(9) x = -5, then from (1) we get
(10) y = -8(-5) - 37 or
(11) y = 40 - 37 or
(12) y = 3
Because you used (1) to get y, check your answer using (2).
Is (-5 + 3*3 = 4)?
Is (-5 + 9 = 4)?
Is (4 = 4)? Yes
Answer: The single, unique solution is (-5,3).
|
|
|
