# How do you solve the system 1/3x-y=3 and 2x+y=25 using substitution?

Oct 2, 2017

$x = 12$ and $y = 1$

#### Explanation:

Given equations are:

(1) ------ $\frac{1}{3} x - y = 3$

(2)------$2 x + y = 25$

Multiply (1) by 3 to eliminate the fractional part,

(1) ------- $x - 3 y = 9$

$\implies x = 9 + 3 y$ -------- let this be equation (3)

Now substitute this value of $x$ from (3) in equation (2),

(2) --------- $2 \left(9 + 3 y\right) + y = 25$

$\implies 18 + 6 y + y = 25$

$\implies 7 y = 25 - 18$

$\implies y = \frac{7}{7}$

Therefore,

$y = 1$

Substituting this value of $y$ in equation (3),

$x = 9 + 3 \setminus \times 1$

$x = 9 + 3$

Therefore,
$x = 12$
So we have the values of $x$ and $y$ as,

$x = 12$ and $y = 1$