How do solve the following linear system?: # -x+3y=-5 , 2x+7=-5y #?

1 Answer
Tony B
Mar 19, 2016

I have taken you to a point where you can solve for #x#
#color(red)(y=-17/11)#

Explanation:

Given:
#-x+3y= -5# ...............................(1)
#2x+7=-5y#.................................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To solve a single equation you can only do so it contains only one unknown. So to solve any of these two we need to 'get rid of a variable'

Look at equation (1). We have a single #x#. So this is the simpler of the two to use as a source of values for substitution.

#color(blue)("Solving for y")#

Consider equation (1)

Multiply by (-1) to make the #x# positive

#x-3y=+5#

Add #3y# to both sides

#color(green)(x=3y+5)" "............................(1_a)#

Substitute for #x# in equation (2) using equation #(1_a)#

#color(brown)(2x+7=-5y" "color(blue)(->" "2(color(green)(3y+5))+7=-5y)#

#6y+10+7=-5y#

#6y+5y=-17#

#color(red)(y=-17/11)# ...................................(3)
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Substitute equation (3) into equation (1) or (2). You chose!

I will let you finish this off.

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