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

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

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Answer 1 · 2018-06-22T20:54:28

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

Explanation:

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

$x+3y=1$

$rArrcolor(blue)(x=1-3y)$

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

$2color(blue)(x)-y=4$

$2color(blue)((1-3y))-y=4$

$2-6y-y=4$

$2-7y=4$

$-7y=2$

$color(green)(y=-2/7)$

We now have a solution for $y$ . We can then plug it into either expression to solve for $x$ :

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

$x+3color(green)((-2/7))=1$

$x-6/7=1$

$x=1+6/7$

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

And now we have our solution:

$x=13/7$ , $y=-2/7$

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

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

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