# Math Help - simultaneous equations!!

1. ## simultaneous equations!!

please i need help with the processes of these two simultaneous equations!!:

7x + 2y = -4
3x + 4y = 14

and...

x/2 + y/3 = 5
x/3 + y/4 = 1

2. Originally Posted by lauqui
please i need help with the processes of these two simultaneous equations!!:

7x + 2y = -4
3x + 4y = 14
$7x + 2y = -4$ ...(1)
$3x + 4y = 14$ ...(2)

Working with (1)

$7x + 2y = -4$

$2y = -4-7x$

$y = \frac{-4}{2}-\frac{7x}{2}$

Now sub this into (2)

$3x + 4y = 14$

$3x + 4 \left(\frac{-4}{2}-\frac{7x}{2}\right)= 14$

Can you find x now?

3. Originally Posted by lauqui
x/2 + y/3 = 5
x/3 + y/4 = 1
Use the same process as in my first post.

$\frac{x}{2} + \frac{y}{3} = 5$ ...(1)

$\frac{x}{3} + \frac{y}{4} = 1$ ...(2)

Working on (1)

$\frac{x}{2} + \frac{y}{3} = 5$

$\frac{y}{3} = 5 - \frac{x}{2}$

$y = 15 - \frac{3x}{2}$

Now into (2)

$\frac{x}{3} + \frac{15 - \frac{3x}{2}}{4} = 1$

You can take it from here....

Once you have a solution for x substittue this into either (1) or (2) to find y.

4. Originally Posted by lauqui
7x + 2y = -4 [1]
3x + 4y = 14 [2]
This is another way, known as the "elimination" process:

Multiply [1] by -2:
-14x - 4y = 8
3x + 4y = 14 [2]

Add them up:
-11x = 22
x = -2 ; next get y by substituting.

Just so you have a headstart on your teacher !