# How do you solve the following system: 2x-y/2=4, -6x-2y=-14 ?

May 17, 2017

The answer will be $x = \frac{15}{7} \mathmr{and} y = \frac{4}{7}$

#### Explanation:

Firstly, simplify both the equations so that you can solve them easily.

Multiply both the sides of the first equation by $2$

$\left(2 x - \frac{y}{2} = 4\right) \times 2$ to get $\text{ } 4 x - y = 8$

Then divide both the sides of the second equation by $- 2$

$\left(- 6 x - 2 y = - 14\right) \div - 2$ to get $\text{ } 3 x + y = 7.$

Now both the equations are simplified.

Solve them by the simultaneous equation method as both of them are Linear equations.

$4 x - y = 8$
$\underline{3 x + y = 7}$
$7 x \text{ " =15" }$ (+ y and -y add to $0$)

$\therefore x = \frac{15}{7}$

Now substitute the value of $x$ into any of the above equations to get the value of y.

$4 x - y = 8 \text{ } \rightarrow 4 \left(\frac{15}{7}\right) - y = 8$
$\frac{60}{7} - y = 8$
$- y = 8 - \frac{60}{7}$

$y = \frac{60}{7} - 8$

$y = \frac{60 - 56}{7}$

$y = \frac{4}{7}$

Hence you get the values.In order to check whether the answers are correct or not you can substitute them in any of the above equations.
If they satisfy the equation, then the answer is correct.😊