# How do you solve the following system: 8x-3y=3, x+3y=3 ?

May 13, 2018

This ordered pair is $\left(\frac{2}{3} , \frac{7}{9}\right)$ or $\left(0. \overline{6} , 0. \overline{7}\right)$.

#### Explanation:

Use the elimination method, and then substitution to solve. Line up the two equations, one on top of the other:

$8 x - 3 y = 3$
$\textcolor{w h i t e}{8}$$x + 3 y = 3$

Now add them together, and notice that $y$ will be eliminated because $- 3 y + 3 y = 0$:

$8 x \textcolor{b l u e}{- 3 y} = 3$
$\textcolor{w h i t e}{8}$$x \textcolor{b l u e}{+ 3 y} = 3$

$\textcolor{w h i t e}{x} 9 x \textcolor{w h i t e}{+ 0 y} = 6$

$9 x = 6$

$x = \frac{6}{9} \rightarrow \frac{2}{3}$

Now substitute that value for $x$ into another equation, and solve for $y$:

$x + 3 y = 3$

$\frac{2}{3} + 3 y = 3$

$2 + 3 \left(3\right) y = 3 \left(3\right)$

$2 + 9 y = 9$

$9 y = 7$

$y = \frac{7}{9}$

So this ordered pair is $\left(\frac{2}{3} , \frac{7}{9}\right)$. As a repeating decimal, the coordinates are $\left(0. \overline{6} , 0. \overline{7}\right)$.

May 13, 2018

Solution: $x = \frac{2}{3} \mathmr{and} y = \frac{7}{9}$

#### Explanation:

8 x-3 y=3 ; (1) , x +3 y =3; (2) , adding equation (1)

and equation (2) we get, $9 x = 6 \therefore x = \frac{6}{9} \mathmr{and} x = \frac{2}{3}$

Putting $x = \frac{2}{3}$ in equation (2) we get, 2/3 +3 y =3;  or

$3 y = 3 - \frac{2}{3} \mathmr{and} 3 y = \frac{7}{3} \mathmr{and} y = \frac{7}{9}$

Solution: $x = \frac{2}{3} \mathmr{and} y = \frac{7}{9}$ [Ans]