How do you solve the following system: 7y - 2x = 10, 11y + 3x = 4 ?

Jul 17, 2017

Arrange your equations, finding $x = - \frac{82}{43}$ and $y = \frac{38}{43}$

Explanation:

Enlarge the first equation with 3 and the second with 2:

$21 y - 6 x = 30$
$22 y + 6 x = 8$

Combine these equations:

$21 y + 22 y = 38$

$43 y = 38$

$y = \frac{38}{43}$

Now you can find x, put this y value into any original equation

$21 \times \left(\frac{38}{43}\right) - 6 x = 30$

$- 6 x = 30 - \left(\frac{798}{43}\right)$

$- 6 x = \frac{492}{43}$

$x = - \frac{492}{43 \times 6}$

$x = - \frac{82}{43}$