How do you solve by substitution $x + 3 y = 5$ $x + 3y = 5$ and $4 x + 5 y = 13$ $4x + 5y = 13$ ?

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How do you solve by substitution $x + 3 y = 5$ $x + 3y = 5$ and $4 x + 5 y = 13$ $4x + 5y = 13$ ?

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Answer 1 · 2015-06-08T18:30:42

$x + 3 y = 5$ $x+3y=5$
$x = 5 - 3 y$ $color(blue)(x=5-3y$ ( we substract $3 y$ $3y$ on each side )

Now that we have $x$ $color(blue)x$ , we can substitute it in the second equation :

$4 x + 5 y = 13$ $4color(blue)x+5y=13$
$4 \cdot (5 - 3 y) + 5 y = 13$ $4*color(blue)((5-3y))+5y=13$
$20 - 12 y + 5 y = 13$ $20-12y+5y=13$
$20 - 7 y = 13$ $20-7y=13$
$20 = 13 + 7 y$ $20=13+7y$ ( we add $7 y$ $7y$ on each side )
$20 - 13 = 7 y$ $20-13=7y$
$7 y = 7$ $7y=7$
$y = 1$ $color(red)(y=1$ ( we divide by $7$ $7$ on each side )

Now that we have $y$ $color(red)y$ , we can find $x$ $color(blue)x$ :

$x = 5 - 3 y$ $color(blue)x=5-3color(red)y$
$x = 5 - 3 \cdot 1$ $color(blue)x=5-3*1$
$x = 5 - 3$ $color(blue)x=5-3$
$x = 2$ $color(blue)(x=2)$

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How do you solve by substitution $x + 3 y = 5$ $x + 3y = 5$ and $4 x + 5 y = 13$ $4x + 5y = 13$ ?

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How do you solve by substitution x + 3y = 5x+3y=5x + 3y = 5 and 4x + 5y = 134x+5y=134x + 5y = 13?

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How do you solve by substitution $x + 3 y = 5$ $x + 3y = 5$ and $4 x + 5 y = 13$ $4x + 5y = 13$ ?