# Simultaneous Linear equation help

### Simultaneous Linear equation help

Hello,

5x - 3y =26 (equation 1)
4x + 2y =34 (equation 2)

I have very little knowledge of these and have tried my hardest to understand how to solve (using substitution), but I cant seem to figure it out.

From what I do understand, there must be a common coefficient within the 2 equations...my idea was to multiply equation 1 by 2 and equation 2 by 3, both resulting in 6y.

At this point I get lost and am not sure if that actually the correct way going about it.

If someone could please explain I would be very much grateful
Guest

### Re: Simultaneous Linear equation help

I would multiply the second equation by 3/2

$$4x + 2y =34$$
$$(4x + 2y)\frac{3}{2} =34 \cdot \frac{3}{2}$$

$$6x + 3y = 51$$

Now we have

$$5x - 3y =26$$ (equation 1)
$$6x + 3y = 51$$ (equation 2)

We can add the both equations

$$5x - 3y + 6x + 3y = 26 + 51$$
$$11x = 77$$
$$x=7$$

Can you find y now?
Guest

### Re: Simultaneous Linear equation help

5x - 3y =26 (equation 1)
4x + 2y =34 (equation 2)

I have very little knowledge of these and have tried my hardest to understand how to solve (using substitution), but I cant seem to figure it out.

From what I do understand, there must be a common coefficient within the 2 equations...my idea was to multiply equation 1 by 2 and equation 2 by 3, both resulting in 6y.

Good! If you do that the first equation, multiplied by 2, becomes 10x- 6y= 52 and the second equation, multiplied by 3, becomes 12x+ 6y= 102.

Now you have
10x- 6y= 52 and
12x+ 6y= 102

Do you see that if you now add these equation
(10x+ 12x)+ (-6y+ 6y)= 52+ 102, the "y" terms cancel leaving
22x= 154.

Divide both sides by 22 to get x= 154/22= 7.
With x= 7, 5x- 3y= 35- 3y= 26 so -3y= 26- 35= -9 so y= -9/-3= 3.

Always check: with x= 7 and y= 3,
5x- 3y= 35- 9= 26 and 4x+ 2y= 28+ 6= 34!
Guest

### Re: Simultaneous Linear equation help

Yet another way to do this:

Solve the equation 4x + 2y =34 for y:
2y= 34- 4x
y= 17- 2x.

Replace y in the other equation by that:
5x - 3y = 5x- 3(17- 2x)= 5x- 51+ 6x= 11x- 51= 26
11x= 26+ 51= 77
so x= 7. Then y= 17- 2(7)= 17- 14= 3.
Guest