How do you solve the following system?: -x -6y =-1, 3x -y = -4−x−6y=−1,3x−y=−4

1 Answer
seph
Nov 17, 2015

See explanation

Explanation:

Isolate one variable in one the equations. Then use the resulting equivalent to replace the same variable in the other equation

-x - 6y = -1−x−6y=−1
3x - y = -43x−y=−4

If we isolate xx in the first equation, we will have

-x - 6y = -1−x−6y=−1
=> x = -6y + 1⇒x=−6y+1

Now, let's replace xx in the second equation

3x - y = -43x−y=−4
=> 3(-6y + 1) - y = -4⇒3(−6y+1)−y=−4
=> -18y + 3 - y = -4⇒−18y+3−y=−4
=> -19y + 3 = -4⇒−19y+3=−4
=> -19y = -7⇒−19y=−7
=> y = 7/19⇒y=719

Now that we have the value for yy, substitute it into any of the equalities above to get xx

x = -6y + 1x=−6y+1
=> x = -6(7/19) + 1⇒x=−6(719)+1
=> x = -42/19 + 1⇒x=−4219+1

=> x = (-42 + 19)/19⇒x=−42+1919

=> x = -23/19⇒x=−2319

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