# How do you solve the following system: 10y=42+2x , 2x-4y=6 ?

Jul 13, 2017

Put both equations in the same form and add or subtract to eliminate x then solve for y

#### Explanation:

Change the first equation to put x and y on the same side

$10 y - 2 x = 42 + 2 x - 2 x$ gives

$10 y - 2 x = 42$

Use the commuative property to change the second equation

$2 x - 4 y = 6 : - 4 y + 2 x = 6$

$10 y - 2 x = 42$
$\pm 4 y + 2 x = 6$ This gives

$6 y = 48$ divide both sides by 6

$6 \frac{y}{6} = \frac{48}{6}$ so

$y = 6$ Put 6 in for y and solve for x

$10 \times 6 = 42 + 2 x$

$60 = 42 + 2 x$ subtract 42 from both sides

$60 - 42 = 42 - 42 + 2 x$ which gives

$18 = 2 x$ divide each side by 2

$\frac{18}{2} = 2 \frac{x}{2}$ so

$9 = x$