How do you solve 4x - 3y = 33 and x = - 4y - 25?

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Answer 1 · 2016-04-25T16:09:31

Point of intersection (lines cross) #->(x,y)=(3,-7)#

Given:

#4x-3y=33#.................................(1)
#x=-4y-25#.................................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the common value of y")#

Using equation (2) substitute for #x# in equation (1)

#4(-4y-25)-3y=33color(white)(.).........................(1_a)#

#-16y-100-3y=33#

#-19y-100=33#

Multiply both sides by (-1)

#+19y+100=-33#

Subtract 100 from both sides

#19y+0=-133#

Divide both sides by 19

#color(blue)(y=-133/19 = -7)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the common value of "x)#

Substitute the value of #y# into equation (2)

#color(brown)(x=-4y-25)" "color(green)( ->" " x=-4(-7)-25)#

#color(blue)(x=+3)#
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