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

1 Answer
Ben
Jun 22, 2018

Solve for one term with respect to another, then solve for the second term, then back-solve for the first. You will find that x=13/7x=137 and y=-2/7y=−27

Explanation:

First, we'll want to solve for either xx in terms of yy or vice versa. For the sake of argument, we'll sove for xx in terms of yy using the second expression:

x+3y=1x+3y=1

rArrcolor(blue)(x=1-3y)⇒x=1−3y

Now, we take that solution for xx and substitute it in, in expression 1:

2color(blue)(x)-y=42x−y=4

2color(blue)((1-3y))-y=42(1−3y)−y=4

2-6y-y=42−6y−y=4

2-7y=42−7y=4

-7y=2−7y=2

color(green)(y=-2/7)y=−27

We now have a solution for yy. We can then plug it into either expression to solve for xx:

x+3color(green)(y)=1x+3y=1

x+3color(green)((-2/7))=1x+3(−27)=1

x-6/7=1x−67=1

x=1+6/7x=1+67

color(green)(x=13/7)x=137

And now we have our solution:

x=13/7x=137, y=-2/7y=−27

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