How do you solve #2p+5q=9, 3p-2q=4#?

1 Answer
Apr 8, 2018

Answer:

#p = 38/19# and #q = 1#

Explanation:

#2p + 5q = 9 color(white)(..) ……(1)#
#3p - 2q = 4 color(white)(..) ……(2)#

Multiply equation #(1)# by #2# and equation #(2)# by #5#

#4p + 10q = 18#
#15p - 10q = 20#

Add both the equations

#4p + 10q + 15p - 10q = 18 + 20#

#19p = 38#

#color(blue)(p = 38/19)#

Substitute #p = 38/19# in equation #(1)#

#2(38/19) + 5q = 9#

#76/19 + 5q = 9#

#5q = 9 - 76/19#

#5q = (9 × 19/19) - 76/19#

#5q = 171/19 - 76/19#

#5q = (171 - 76)/19#

#5q = 95/19#

#q = 95/(19 × 5) = 95/95#

#color(blue)(q = 1)#