How do you solve the following system?: #-1/2x+5y=-20 , y=1-3x #

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Answer 1 · 2016-01-10T14:07:45

Answer given in extreme detail so that you can see what is happening. With practise you should be able to do this in 4 to 5 lines.

#color(blue)(color(white)(...)(x,y) -> (1 19/31 ,3 26/31)#

Tony B

Given:
#-1/2x+5y=-20.....................................(1)#
#y=1-3x..................................................(2)#

#color(blue)("To find the value of x")#

Substitute for y in (1) using (2)

#-1/2x +5(1-3x)=-20...........................(1_a)#

Multiplying out the brackets
#-1/2 x-15x+5=-20#

Adding the x-terms
#-31/2 x+5=-20#

Collecting like terms
#-31/2x=-25#

Multiply both sides by 2
#-31x=-50#

Multiply both sides by (-1)
#31x=50#

Divide both sides by 31
#x=50/31..........................................(3)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the value of y")#

Substitute equation (3) into equation (2) giving

#y=1-3x -> y=1-3(50/31)#

#y=1 - 150/31#

#y=-119/31 =-3 26/31#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

The point of intersection of the two graphs/equations is:

#(x,y) -> (1 19/31 ,3 26/31)#