How do you solve x= 3y-1 and x+2y=9 using substitution?

Mar 6, 2018

$\left(5 , 2\right)$

Explanation:

You know the value of the variable $x$, so you can substitute that into the equation.
${\overbrace{\left(3 y - 1\right)}}^{x} + 2 y = 9$

Remove the parentheses and solve.
$3 y - 1 + 2 y = 9$

$\implies 5 y - 1 = 9$

$\implies 5 y = 10$

$\implies y = 2$

Plug $y$ into either equation to find $x$.
$x = 3 {\overbrace{\left(2\right)}}^{y} - 1$

$\implies x = 6 - 1$

$\implies x = 5$

$\left(x , y\right) \implies \left(5 , 2\right)$

Mar 6, 2018

$x = 5 , y = 2$

Explanation:

Given $x = 3 y - 1 \mathmr{and} x + 2 y = 9$

Substitute $x = 3 y - 1$ into $x + 2 y = 9$,

$\left(3 y - 1\right) + 2 y = 9$
$5 y - 1 = 9$
$5 y = 10$
$y = 2$

Substitute y=2 into the first equation,
$x = 3 \left(2\right) - 1$
$x = 5$

Mar 6, 2018

$x = 5$
$y = 2$

Explanation:

If

$x = 3 y - 1$

then use that equation in the second equation. This means that

$\left(3 y - 1\right) + 2 y = 9$

$5 y - 1 = 9$

$5 y - 1 + 1 = 9 + 1$

$5 y = 10$

$\frac{5 y}{5} = \frac{10}{5}$

$y = 2$

Having said this, just replace the $y$ in the first equation in order to get the $x$.

$x = 3 \left(2\right) - 1$

$x = 6 - 1$

$x = 5$

After that, just check that the values make sense:

$x = 3 y - 1$

$5 = 3 \left(2\right) - 1$

$5 = 6 - 1$

$5 = 5$

And for the second one:

$x + 2 y = 9$

$5 + 2 \left(2\right) = 9$

$5 + 4 = 9$

$9 = 9$

Both answers satisfy both equations, which makes them correct.