How do you solve the system of equations: 5x + 3y = 12 ; 4x - 5y = 17?

1 Answer
Aug 22, 2015

Answer:

The solutions are
#color(blue)(y=-1,x=3#

Explanation:

#5x + 3y = 12#, multiplying by #4#
#color(blue)(20x) + 12y = 48#....equation #1#

# 4x - 5y = 17#, multiplying by #5#
# color(blue)(20x) - 25y = 85#.....equation #2#

Solving by elimination

Subtracting equation #1# from #2#

#cancelcolor(blue)(20x) + 12y = 48#
# cancel(-color(blue)(20x)) + 25y = -85#

#37y=-37#
#color(blue)(y=-1#

Finding #x# from equation #1#
#5x + 3y = 12#

#5x = 12-3y#

#5x = 12+3#

#5x = 15#
#color(blue)(x=3#