# How do you solve the simultaneous equations  4x - 2y = 6  and 3x + y = 17?

May 15, 2018

You can isolate one of the variables in one of your equations and plug it into the second. X equals 4.

#### Explanation:

Isolate one of the variables in one of the equations. Here, it's easier to isolate the y of the second equation.
$3 x + y = 17$
$y = 17 - 3 x$

Now, you can plug in what you got for y into the FIRST equation.
$4 x - 2 y = 6$
$4 x - 2 \left(17 - 3 x\right) = 6$

$4 x - 34 + 6 x = 6$
$4 x + 6 x = 6 + 34$
$10 x = 40$

Solve for x.
$x = \frac{40}{10}$
$x = 4$

May 15, 2018

y = 5, while x = 5

#### Explanation:

Let

A: $4 x - 2 y = 6$
B: $3 x + y = 17$

Then rearrange B to get it in terms of y, since it already has y on it's own.

Thus gives us B: $y = 17 - 3 x$

Then substitute this value of y into equation A:

thus we get $4 x - 34 + 6 x = 6$

if we rearrange this, we get $x = 4$

If we put this into the rearrange form of B: we get $y = 5$