1. ## Simultaneous linear equations

2y - x = 7

y + 2x = 1

After trying over and over i now know x=-1 and y = 3 but cant prove the math to show working, sort of stumbled on it
ive gone over it time and time again but im baffled

many thanks

2. 2Y - X = 7 equation 1
Y + 2X = 1 equation 2

Mutiply the second equation by 2 to get:

2Y + 4X = 2

Minus this new equation from the first equation:

(2Y - X = 7) - (2Y +4X = 2)

The ys cancel out leaving you with:

-5x = 5
so x= 1

subsitute this back into thte second equation:
y + 2 = 1
y = -1

hope this helps

3. Please ignore me if im making an idiot out of myself here, but i see how those results relate to equation 2, but not to equation 1, i;m very new to this type of math so im still learnering the rules of it to a large extent.

many thanks for your help by the way

4. sorry thats my fault. Let me try again.

The ys cancel out leaving you with:

-5x = 5
so x= -1

subsitute this back into the second equation:
y - 2 = 1
y = 3

to check we can substitute this into equation 1:

2(3) - (-1) = 7
6 + 1 = 7

hope this helps again

5. Now it all makes sense ha ha thank you William, very much appreciated

6. ah problem, the method used appears to be the method of equating co-efficients, i need to use the solution by substitution

7. ## Updated!!!

How does this look?

Equation 1 - 2y - x = 7

Equation 2 - y + 2x = 1

E1) x = 7 - 2y

E2) y + 2(7 - 2y) = 1
E2) y + 14 - 4y = 1
E2) 14 - 5y = 1
E2) 5y = 14 +1
E2) 5y = 15
E2) 15/5 = 3
y = 3

Substitute in E1

2y - x = 7
6 - x = 7
6 - 7 = x
x = -1

Equation 1 = 2y - x = 7

2 x 3 - (-1) = 7
6 - (-1) = 7

Equation 2 = y + 2x = 1

3 + (2 x -1) = 1
3 -(-2) = 1

???