SOLUTION: How many solutions are there to this: y=-8x-37, x+3y=4

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).

RELATED QUESTIONS
how many solutions are there to the math problem y�= 4/3y=5/4. thank... (answered by Fombitz)

How many solutions are there to this: 2x=3y-9 ,... (answered by musicmaster4)

how many real solutions are there for 0= x to the second power + 8x +... (answered by checkley71)

How many solutions are there to this: 4x-y-4=0 ,... (answered by lynnlo)

How many solutions are there to this: 4x-y-4=0 ,... (answered by Alan3354)

How many solutions are there to this system? Please provide all steps. 4x - 7y = 15... (answered by TimothyLamb)

How many solutions are there for this equation? 2y = 2x + 24 -x + y =... (answered by lmeeks54)

How many solutions are there to the quadratic equation 4x2 + 8x + 3 = 0? (answered by checkley75)

Hi I need help with this- How many solutions are there to the following system equations: (answered by KMST)