How do you find the number of solutions of #-5y + 40= 16x# and #y = \frac { - 16} { 5} x + 8# without graphing?

Question

426 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-22T15:26:06

Thus there is an infinite number of solutions that they shair

Given:

#-5y+40=16x" "...................Equation(1)#
#y=(-16)/5x+8" ".....................Equation(2)#

Consider #Equation(1)#

I am going to make it into the same form as #y=ax+c#

Multiply everything by (-1) to make the #y# term positive.

#+5y-40=-16x#

Add 40 to both sides

#5y=-16x+40#

Divide both sides by 5

#y= -16/5x+8" "................Equation(1_a)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Observe that both #Equation(1) and Equation(2)# are different formats of the same equation.

Thus there is an infinite number of solutions that they shair