# How do you solve the following system: 2x+7y=1, 6x + 7y = -9 ?

Jul 31, 2017

By arranging it, it can be calculated that $x = - \frac{5}{2}$ and $y = \frac{6}{7}$

#### Explanation:

The first equation can be rewritten
$- 6 x - 21 y = - 3$ (after multiplication by -3)
$6 x + 7 y = - 9$ (the second original equation)

Combine these two equations:
$- 14 y = - 12$

$y = \frac{12}{14}$
or
$y = \frac{6}{7}$

Now put value in the first original equation:

$2 x = 1 - \left(7 \times \left(\frac{6}{7}\right)\right)$

$2 x = 1 - 6$

$x = - \frac{5}{2}$

The answer is $x = - \frac{5}{2}$ and $y = \frac{6}{7}$

Jul 31, 2017

$x = - 2.5 \mathmr{and} y = \frac{6}{7}$

#### Explanation:

Note that the number of $y$s in both equations stays the same.
The difference in the the totals therefore represents the difference in the number of $x$s. Subtract the two equations:

$\text{ "6xcolor(blue)(+7y) =-9" } \ldots \ldots \ldots A$
$\text{ "ul(2xcolor(blue)(+7y) =+1)" } \ldots \ldots \ldots B$

$A - B \text{ "4x = -10" }$solve for $x$

$\text{ } x = - 2.5$

Substitute $- 2.5$ for $x$ to find $y$ in B

$2 \left(- 2.5\right) + 7 y = 1$

$\text{ } - 5 + 7 y = 1$
$\text{ } 7 y = 1 + 5$
$\text{ } 7 y = 6$
$\text{ } y = \frac{6}{7}$

Check in A:
$6 \times \left(- 2.5\right) + 7 \left(\frac{6}{7}\right)$

$= - 15 + 6 = - 9$
This is correct.