How do you solve this system of equations: #3x + 5y = 19 and 4x - y = 10#?

1 Answer
Nov 28, 2017

Answer:

#x=3 and y=2#

Explanation:

I will solve your system by substitution (you can also solve this system by elimination).

#4x−y=10#
#3x+5y=19#

Step: Solve #4x−y=10# for #y#:

#4x−y+−4x=10+−4x" "# (add #-4x# to both sides)

#−y=−4x+10#

Divide by #-1#

#y=4x−10#

Step: Substitute #4x−10# for #y# in #3x+5y=19#:

#3x+5y=19#

#3x+5 (4x−10)=19#

#23x−50=19 " "#(simplify both sides of the equation)

#23x−50+50=19+50 " "#(add #50# to both sides)

#23x=69#

Divide both sides by #23#

#x=3#

Step: Substitute #3# for #x# in #y=4x−10#:

#y=4x−10#

#y=(4)(3)−10#

#y=2" "# (simplify both sides of the equation)