How do you solve the system $4 x - y = 5$ $4x - y = 5$ and $x + y = 10$ $x + y = 10$ ?

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How do you solve the system $4 x - y = 5$ $4x - y = 5$ and $x + y = 10$ $x + y = 10$ ?

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Answer 1 · 2015-06-08T18:16:09

$x + y = 10$ $x+y=10$
Thus : $x = 10 - y$ $color(blue)(x=10-y$ ( we substract $y$ $color(red)y$ on each side )

We can now replace it in the first equation :

$4 x - y = 5$ $4color(blue)x-y=5$
$4 \cdot (10 - y) - y = 5$ $4*color(blue)((10-y))-y=5$
$40 - 4 y - y = 5$ $40-4y-y=5$
$40 - 5 y = 5$ $40-5y=5$
$40 = 5 + 5 y$ $40=5+5y$ ( we add $5 y$ $5y$ on each side )
$40 - 5 = 5 y$ $40-5=5y$ ( we substract $5$ $5$ on each side )
$35 = 5 y$ $35=5y$
$y = 7$ $color(red)(y=7$ ( we divide by $5$ $5$ on each side )

We can now calculate $x$ $color(blue)x$ with $y$ $color(red)y$ :

$x = 10 - y$ $color(blue)x=10-color(red)y$
$x = 10 - 7$ $color(blue)x=10-color(red)7$
$x = 3$ $color(blue)(x=3)$

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How do you solve the system $4 x - y = 5$ $4x - y = 5$ and $x + y = 10$ $x + y = 10$ ?

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