How do you solve the system of equations #2x + 5y = 6# and #- 2x - 3y = 6#?

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Answer 1 · 2017-09-06T11:43:57

#x=-12#
#y=6#

Finding x is gonna be a bit long so here it is:

Label #2x+5y = 6# and #-2x-3y = 6# as Equation 1 and 2 respectively.

Seeing as the #y# variables aren't equal, multiply Eq. 1 by 3 to get #15y# and multiply Eq.2 by 5 to get #-15y#:

Eq 1 * 3:
#6x + 15y = 18#

Eq 2 * 5
#-10x - 15y = 30#

Label these new equations as Eq 3 and 4, respectively.

Add these two equations together:
Eq. 3 + Eq. 4

#6x + 15y = 18#
#-10x - 15y = 30#

#=-4x = 48#
#x = -12#

To find y, substitute the value of x into one of the equations:
#2(-12)+5y =6#
#-24 + 5y = 6#
#5y = 6+24#
#5y = 30#
#y=6#

Hope this helps!