How do you solve the following system: #5x - 7y = 12 , x + 8y = 15 #?

1 Answer
May 21, 2016

Answer:

The solution for the system of equations is:
#color(green)(x=201/47 , y = 63/47#

Explanation:

#color(blue)(5x) - 7y =12#.............equation #(1)#

#x + 8y = 15#, multiplying by #5#
#color(blue)(5x) + 40y = 75# ..........equation #(2)#

Solving by elimination:

Subtracting equation #2# from equation #1:#

#cancelcolor(blue)(5x) - 7y =12#
#-cancelcolor(blue)(5x) - 40y = -75#

#-47 y = -63 #

#y = -63 / (47 )#

#color(green)(y = 63/47#

Finding #x# from equation #2#
#x + 8y = 15#

#x = 15 - 8y #

#x = 15 - 8 * (63/47) #

#x = 15 - 504/47 #

#x = 705 /47 - 504/47 #

#color(green)(x = 201/47 #