Question 315322
<pre><b>
{{{system(5x + 4y = 1,
4x + 3y = -1)}}}

To make the y terms cancel out, multiply
the first equation through by -3 and the
second equation through by +4:

{{{system(red((-3))(5x + 4y) = red((-3))1,
red((""+4))(4x + 3y) = red((""+4))-1)}}}

{{{system(-15x - 12y = -3,
""+16x + 12y = -4)}}}

Add those two equations vertically term by term and get:

{{{x=-7}}}

To make the x terms cancel out, multiply
the first equation through by -4 and the
second equation through by +5:

{{{system(red((-4))(5x + 4y) = red((-4))1,
red((""+5))(4x + 3y) = red((""+5))-1)}}}

{{{system(-20x - 16y = -4,
""+20x + 15y = -5)}}}

Add those two equations vertically term by term and get:

{{{-y=-9}}}
{{{y=9}}}

The solution is (x,y) = (-7,9)

Checking:

{{{system(5x + 4y = 1,
4x + 3y = -1)}}}

{{{system(5(-7) + 4(9) = 1,
4(-7) + 3(9) = -1)}}}

{{{system(-35 + 36 = 1,
-28 + 27 = -1)}}}

{{{system(1 = 1,
-1 = -1)}}}

The solutions check
<pre>