How do I solve simultaneous equations with two variables?

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SUMMARY

The discussion focuses on solving simultaneous equations with two variables, specifically the equations 5p1 - 4p2 = 49 and 3p1 + 2p2 = 3. The user successfully isolates p1 as 5 by manipulating the equations and confirms the value of p2 as -6 by substituting p1 back into both original equations. This method demonstrates the elimination technique for solving simultaneous equations, ensuring accuracy by verifying results through substitution.

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Homework Statement



I am asked to find the two variables in a simulatenous equation. Now I have found one variable but unsure on how to find the other (P2).

Homework Equations


[itex]5p1 - 4p2 = 49[/itex]
[itex]3p1 + 2p2 = 3[/itex]

The Attempt at a Solution



[itex]5p1 - 4p2 = 49[/itex] (Multiply by 2)
[itex]3p1 + 2p2 = 3[/itex] (Multiply by 4)

[itex]10p1 = 98[/itex]
[itex]12p1=12[/itex]

Add the two together

[itex]22p1=110[/itex]
[itex]p1=5[/itex] (110 divided by 22)
 
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plug the value of p1 back into either equation to find p2. Actually, put it back into both to make sure you get the same answer for p2 each time.
 
ArcanaNoir said:
plug the value of p1 back into either equation to find p2. Actually, put it back into both to make sure you get the same answer for p2 each time.

Thank you! I couldn't quite remember what to do.

So what I got was
[itex](5(5) - 49)/4 = -6[/itex]
[itex](5(3) - 3)/2 = -6[/itex]

So [itex]P2 = -6[/itex] Thanks!
 

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