# Question aea82

May 28, 2017

x=2; y=3

#### Explanation:

Solving by elimination causes one unknown term to be removed from the system of equations at a time.

Given:
$3 x + 4 y = 18$
$2 x - 4 y = - 8 \to$ To eliminate the $y$ term, add the two equations:

5x=10; x=2

To eliminate the $x$ term, multiply the two equations so the x term is the same in each (in this system, the multipliers are $2 \mathmr{and} 3$):

$2 \cdot 3 x + 2 \cdot 4 y = 2 \cdot 18$
$3 \cdot 2 x - 3 \cdot 4 y = 3 \cdot \left(- 8\right) \to$

$6 x + 8 y = 36$
$6 x - 12 y = - 24 \to$ then subtract the second equation from the first:

$\cancel{6 x} + 8 y = 36$
$\cancel{- 6 x} - \left(- 12 y\right) = - \left(- 24\right) \to$

20y=60; y=3#

To check, substitute the answers into either equation:

$2 x - 4 y = - 8 \to$

$2 \cdot 2 - 4 \cdot 3 = - 8 \to$

$4 - 12 = - 8$

$- 8 = - 8$