How do I solve simultaneous equations with two variables?

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To solve the simultaneous equations 5p1 - 4p2 = 49 and 3p1 + 2p2 = 3, the first step is to manipulate the equations for easier elimination. By multiplying the first equation by 2 and the second by 4, the equations can be aligned for addition. This results in 22p1 = 110, leading to p1 = 5. Substituting p1 back into either original equation confirms that p2 equals -6. The solution for the variables is p1 = 5 and p2 = -6.
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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


5p1 - 4p2 = 49
3p1 + 2p2 = 3

The Attempt at a Solution



5p1 - 4p2 = 49 (Multiply by 2)
3p1 + 2p2 = 3 (Multiply by 4)

10p1 = 98
12p1=12

Add the two together

22p1=110
p1=5 (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
(5(5) - 49)/4 = -6
(5(3) - 3)/2 = -6

So P2 = -6 Thanks!
 

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