How do you find the solution set for y=6x-5 and y=-x+9?

1 Answer
Stefan V.
Aug 11, 2015

#{(x = 2), (y = 7) :}#

Explanation:

Your system of equations looks like this

#{(y = 6x-5), (y = -x+9):}#

Notice that #y# is said to be equal to two distinct expressions that depend on #x#, which can only mean that these expressions must be equal to each other.

#6x-5 = -x + 9#

Solve this equation for #x#

#6x + x = 9 + 5#

#7x = 14 implies x= 14/7 = color(green)(2)#

Pick any of the two original equations and find the value of #y#

#y = 6 * (2) - 5#

#y = 12 - 5 = color(green)(7)#

The solution set to this system of equations is

#{(x = 2), (y = 7) :}#

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