How do you solve the system: #y = 3x - 5#, #y = -2x - 15#?

1 Answer
Tony B
Feb 23, 2016

#color(blue)("Point of intersection "->(x,y)->(-2,-11)#

Explanation:

When looking at this type of question they are saying that there is one value of x and one value of y that is true for both equations. In other words; the graph lines cross each other. It is at the crossing point the values for x and y are the same for each equation.

As they share the same values you can equate them to other through y in that:

#3x-5" " =" "y" "=" "-2x-15#

Collecting terms we have

#3x+2x=5-15#

#5x=-10#

#x=-2#
'~~~~~~~~~~~~~~~~~~~~
Substitute #x=-2# into any of the original equations to find the value of y

#y=3x-5" "->" "y=3(-2)-5#

#y=-6-5#

#y=-11#
'~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("So point of intersection "->(x,y)->(-2,-11)#

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