How do you solve the following linear system: -2x+5y=4, 3x+8y=1 −2x+5y=4,3x+8y=1?

1 Answer
Alan P.
May 20, 2016

(x,y)=color(blue)(""(-27/31,14/31))(x,y)=(−2731,1431)

Explanation:

Given
[1]color(white)("XXX")-2x+5y=4XXX−2x+5y=4
[2]color(white)("XXX")3x+8y=1XXX3x+8y=1

To eliminate the xx components we can convert the given equations
into ones with identical coefficients for xx
by multiplying [1] by 33 and [2] by 22
[3]color(white)("XXX")-6x+15y=12XXX−6x+15y=12
[4]color(white)("XXX")6x+16y=2XXX6x+16y=2

Adding [3] and [4]
[5]color(white)("XXX")31y=14color(white)("XX")rarrcolor(white)("XX")y=14/31XXX31y=14XX→XXy=1431

We cold plug this value back into one of the original equations and solve for xx
or (the method I find simpler in this case) repeat the above process to eliminate yy from the original given equations.
[6]color(white)("XXX")-16x+40y=32XXX−16x+40y=32
[7]color(white)("XXX")15x+40y=5XXX15x+40y=5

Subtracting [7] from [6]
[8]color(white)("XXX")-31x = 27color(white)("XX")rarrcolor(white)("XX")x=-27/31XXX−31x=27XX→XXx=−2731

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