How do you solve the following linear system # 3 x-2y=4 , x+4y=3#?

2 Answers
Feb 12, 2017

Answer:

# y = 5/14 #
# x = 11/7 #

Explanation:

1) Rearrange your equations to make them easier to use. The easiest way to do this is to isolate ONE variable that has the coefficient of 1.

# 3x - 2y = 4 #

# x = -4y + 3 #

2) Since you now know what the x variable is in terms of y, you can go ahead and substitute it into the first equation.

# 3 (-4y + 3) - 2y = 4 #

3) Simplify

# 3 (-4y + 3) - 2y = 4 #

# -12y + 9 - 2y = 4 #

# -14y + 9 = 4 #

# -14y = -5 #

# y = 5/14 #

4) Substitute the solution you just got to get the second variable.

# x + 4y = 3 #

# x + 4 (5/14) = 3 #

# x + 10/7 = 3 #

# x = 11/7 #

Feb 12, 2017

Answer:

#x=11/7=1 4/7# and #y=5/14#

Explanation:

#3x-2y=4#
#x+4y=3#

Using the second equation, derive a value for #x#.

#x+4y=3#

Subtract #4y# from each side.

#x=3-4y#

In the first equation, substitute #x# with #color(red)((3-4y))#.

#3x-2y=4#

#3color(red)((3-4y))-2y=4#

Open the brackets and simplify. The product of a positive and a negative is a negative.

#9-12y-2y=4#

#9-14y=4#

Subtract #9# from each side.

#-14y=-5#

Divide both sides by #-14#.

#y=5/14#

In the second equation, substitute #y# with #color(blue)(5/14)#.

#x+4y=3#

#x+4(color(blue)(5/14))=3#

Open the brackets and simplify.

#x+2cancel4xx5/(7cancel14)=3#

#x+10/7=3#

Subtract #10/7# from each side.

#x=3-10/7#

#x=21/7-10/7#

#x=11/7=1 4/7#