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#
