How do you solve the system $x=3y$ and $3x-5y=12$ using substitution?

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Answer 1 · 2017-03-28T14:35:07

See the entire solution process below:

Step 1) Because the first equation is already solved for $x$ we can substitute $3y$ for $x$ in the second equation and solve for $y$ :

$3x - 5y = 12$ becomes:

$(3 xx 3y) - 5y = 12$

$9y - 5y = 12$

$(9 - 5)y = 12$

$4y = 12$

$(4y)/color(red)(4) = 12/color(red)(4)$

$(color(red)(cancel(color(black)(4)))y)/cancel(color(red)(4)) = 3$

$y = 3$

Step 2) Substitute $3$ for $y$ in the first equation and calculate $x$ :

$x = 3y$ becomes:

$x = 3 xx 3$

$x = 9$

The solution is: $x = 9$ and $y = 3$ or $(9, 3)$

How do you solve the system x=3yx=3y and 3x-5y=123x-5y=12 using substitution?