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

Hence the solution is
-=(x,y)=-=(4.41,-0.559

#### Explanation:

$3 x + 4 y = 11$-----(1)
$x - 10 y = 10$-----(2)
$x + 1.333 y = 3.667$------(3)=(1)/3
$- 11.333 y = 6.333$-----(4)=(2)-(3)
$y = - 0.559$-------(5)=(4)/-11.333
Substituting in (2)
$x - 10 \times \left(- 0.559\right) = 10$
$x + 5.590 = 10$
$x = 10 - 5.59$
$x = 4.41$
Check:
$3 x + 4 y = 3 \left(4.41\right) + 4 \left(- 0.559\right) = 11$verified
$4.41 - 10 \left(- 0.559\right) = 10$verified
Hence the solution is
-=(x,y)=-=(4.41,-0.559

Mar 2, 2018

$x = \frac{75}{17}$, $y = - \frac{19}{34}$

#### Explanation:

(1) $3 x + 4 y = 11$
(2) $x - 10 y = 10$

Solving (2) for x:
(3) $x = 10 y + 10$

Substituting (3) into (1):
$3 \left(10 y + 10\right) + 4 y = 11$

$30 y + 30 + 4 y = 11$

$34 y = - 19$

(4) $y = - \frac{19}{34}$

Substituting (4) into (2):
$x - 10 \left(- \frac{19}{34}\right) = 10$

$x + \frac{95}{17} = \frac{170}{17}$

$x = \frac{75}{17}$

(5) $x = \frac{75}{17}$