How do you solve #2a + 3b = -1# and #3a + 5b = -2#?

1 Answer
Aug 21, 2015

Answer:

The solutions are
#color(blue)(a=1,b=-1#

Explanation:

# 2a+3b=−1 #, multiplying the equation by #3#
# color(blue)(6a)+9b=−3 #..........equation #1#

# 3a+5b=−2#multiplying the equation by #2#
#color(blue)( 6a)+10b=−4#.......equation #2#

Solving by elimination .
Subtracting equation #2# form #1#

#cancel( color(blue)(6a))+9b=−3 #
#cancel(-color(blue)( 6a))-10b=+4#

#-b=1#
#color(blue)(b=-1#

Substituting #b# in equation #1# to find #a#:
#2a+3b=−1 #
#2a=−1-3b #
#2a=−1-3*(-1) #
#2a=2#
#color(blue)(a=1#