How do you solve 5x+6y=24 and 3x+5y=18?

1 Answer
Sep 6, 2015

Answer:

#{(x = 12/7), (y = 18/7) :}#

Explanation:

Your starting system of equations is

#{(5x + 6y = 24), (3x + 5y = 18):}#

Multiply the first equation by #(-3)# and the second equation by #5# to get

#{(5x + 6y = 24| * (-3)), (3x + 5y = 18| * 5):}#

#{(-15x - 18y = -72), (15x + 25y = 90):}#

Notice that if you add these two equations, more specifically if you add the left-hand sides and the right-hand sides separately, you can eliminate the #x#-term.

This will allow you to solve the resulting equation for #y#

#{(-15x - 18y = -72), (15x + 25y = 90):}#
#stackrel("-------------------------------------------------------")#
#color(red)(cancel(color(black)(15x))) - 18y + color(red)(cancel(color(black)(15x))) + 25y = -72 + 90#

#7y = 18 implies y = color(green)(18/7)#

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

#5x + 6 * 18/7 = 24#

#35x + 108 = 168#

#35x = 60 implies x = color(green)(12/7)#