How do solve the following linear system?: $x+2y=1 , x+y=6$ ?

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Answer 1 · 2015-11-28T04:51:59

$(11, -5)$

Equation 1: $x+2y= 1$
Equation 2 : $x+y= 6$

To solve by substitution method, take equation 1, solve for $x$
$x+2y= 1$ $hArr color(red)( x= 1-2y)$

Then substitute $color(red)(x= 1-2y)$ into equation 2

$=> color(red)((1-2y)) + y = 6$

$=>1-y= 6$
$=> -y= 5$ $=> color(blue)(y = -5)$

Substitute the solution for $y$ into either equation 1 equation 2

$=> x+2color(blue)*((-5))= 1$
$=> x-10 = 1$ $=>color(blue)( x= 11)$

We can verify the solution by substitute the solution into the original equations

Eq 1: $(11)+ 2(-5) = 1$
$=> 1= 1$

Eq 2: $11+(-5) = 6$
$=> 6= 6$

How do solve the following linear system?: x+2y=1 , x+y=6 x+2y=1 , x+y=6 ?