How do you solve 5x + y = -2 and 4x + 7y = 2?

1 Answer
Sep 8, 2015

Answer:

#{(x = -16/31), (y = 18/31) :}#

Explanation:

Take a look at your system of equations

#{(5x + y = -2), (4x+7y = 2) :}#

Notice that if you multiply the first equation by #(-7)# and add the left-hands sides and the right-hand sides of the two equations, you can eliminate the #y#-term.

This will leave you with one equation with one unknown, #x#.

#{(5x + y = -2 | * (-7)), (4x+7y = 2) :}#

#{(-35x -7y = 14), (4x+7y = 2) :}#
#stackrel("-----------------------------------------------")#

#-35x - color(red)(cancel(color(black)(7y))) + 4x + color(red)(cancel(color(black)(7y))) = 14 + 2#

#-31x = 16 implies x = 16/((-31)) = color(green)(-16/31)#

Now use this value of #x# in one of the original two equations to find the value of #y#

#5 * (-16)/31 + y = -2#

#y = -2 + 80/31#

#y = color(green)(18/31)#