How do you solve the following system: 6x + y = 2, 5x + 8y = -2?

1 Answer
Veddesh phi
Apr 10, 2016

(x,y)=(-22/43,18/43)

Explanation:

Solve by elimination substitution

color(blue)(6x+y=2

color(blue)(5x+8y=-2

We can eliminate 8y in the second equation by y in the first equation if we multiply (whole equation) y with -8 to get -8y

rarr-8(6x+y=2)

Use distributive property

color(brown)(a(b+c=x)=ab+ac=ax

rarr-48x-8y=-16

Now,add the above equation to the second equation to eliminate 8y

rarr(-48x-8y=-16)+(5x+8y=-2)

rarr-43x=-18

Divide both sides by -43

rarr(cancel(-43)x)/cancel(-43)=(-18)/-43

color(green)(rArrx=18/43

Because,

color(brown)((-a)/-b=a/b

Now,substitute the value of x to the first equation

rarr6(18/43)+y=2

rarr108/43+y=2

rarr(108+43y)/43=2

Multiply both sides by 43

rarr(108+43y)/cancel43*cancel43=2*43

rarr108+43y=86

Subtract 108 both sides

rarr108+43y-108=86-108

rarr43y=-22

Divide both sides by 43

rarr(cancel43y)/cancel43=-22/43

color(green)(rArry=-22/43

color(blue)(ul bar |(x,y)=(-22/43,18/43)|

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