How do you solve 4x + 3y = - 4 and 3x - 7y = 34?

1 Answer
Jan 29, 2017

Answer:

See the entire solution process below:

Explanation:

Step 1) Solve the first equation for #x#:

#4x + 3y = -4#

#4x + 3y - color(red)(3y) = -4 - color(red)(3y)#

#4x + 0 = -4 - 3y#

#4x = -4 - 3y#

#(4x)/color(red)(4) = (-4 - 3y)/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -4/4 - (3y)/4#

#x = -1 - 3/4y#

Step 2) Substitute #-1 - 3/4y# for #x# in the second equation and solve for #y#:

#3(-1 - 3/4y) - 7y = 34#

#-3 - 9/4y - 7y = 34#

#color(red)(3) - 3 - 9/4y - 7y = color(red)(3) + 34#

#-9/4y - 7y = 37#

#-9/4y - (4/4 xx 7)y = 37#

#-9/4y - 28/4y = 37#

#-37/4y = 37#

#-color(blue)(4)/color(red)(37) xx -37/4y = -color(blue)(4)/color(red)(37) xx 37#

#cancel(-color(blue)(4))/cancel(color(red)(37)) xx color(red)(cancel(color(black)(-37)))/color(blue)(cancel(color(black)(4)))y = -color(blue)(4)/cancel(color(red)(37)) xx color(red)(cancel(color(black)(37)))#

#y = -4#

Step 3) Substitute #-4# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = -1 - (3/4 xx -4)#

#x = -1 - (3/color(red)(cancel(color(black)(4))) xx -color(red)(cancel(color(black)(4))))#

#x = -1 - (-3)#

#x = -1 + 3#

#x = 2#

The solution to this problem is:

#x = 2# and #y = -4#