1. ## Simultaneous equation

Hello, could somebody solve this to find the values for P1 and P2 for me and show how they have worked it out I am struggling a bit with it. Thanks

2P1 - 5P2 = -6
-P1 + 3P2 = 4

2. ## Re: Simultaneous equation

Use "easier" variables:
2a - 5b = -6 [1]
-a + 3b = 4 [2]

Multiply [2] by 2:
-2a + 6b = 8 [2]

Continue by adding the 2 equations...

3. ## Re: Simultaneous equation

Originally Posted by davefrick1
Hello, could somebody solve this to find the values for P1 and P2 for me and show how they have worked it out I am struggling a bit with it. Thanks

2P1 - 5P2 = -6
-P1 + 3P2 = 4
Using your variables, Multiply the second equation by 2 to get
-2P1+ 6P2= 8 and add the first equation
2P1- 5P2= -6

P2= 2. With P2= 2, the second equation is -P1+ 3(2)= -P1+ 6= 4. So -P1= 4- 6= -2 and P1= 2.

4. ## Re: Simultaneous equation

Thank you that was very helpful

5. ## Re: Simultaneous equation

Another way: from $\displaystyle -P_1+ 3P_2= 4$ adding $\displaystyle P_1$ to both sides gives $\displaystyle 3P_2= 4+ P_1$ and then subtracting 4 from both sides gives $\displaystyle 3P_2- 4= P_1$. Now, we can replace $\displaystyle P_1$ with $\displaystyle 3P_2- 4$ in $\displaystyle 2P_1- 5P_2=- 6$: $\displaystyle 2(3P_2- 4)- 5P_2= 6P_2- 8- 5P_2= P_2- 8= -6$ so $\displaystyle P_2= 8- 6= 2$. Then $\displaystyle P_1= 3P_2- 4= 3(2)- 4= 6- 4= 2$.