How do I solve simultaneous equations with two variables?

  • Thread starter lloydowen
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In summary, the conversation discusses finding the two variables in a simultaneous equation. The process involves multiplying both equations by different numbers, adding them together, and solving for the first variable. The second variable can then be found by plugging the value of the first variable back into either equation. The final answer for both variables is -6.
  • #1
lloydowen
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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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  • #2
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.
 
  • #3
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!
 

1. What are simultaneous equations?

Simultaneous equations are a set of two or more equations with multiple variables that are solved at the same time. The solution to the equations is a set of values for each variable that satisfies all of the equations.

2. How do you solve simultaneous equations?

The most common method for solving simultaneous equations is by substitution or elimination. Substitution involves isolating one variable in one equation and substituting it into another equation to find the value of the other variable. Elimination involves manipulating the equations so that when added together, one of the variables is eliminated, leaving only one variable to solve for.

3. Can simultaneous equations have more than two variables?

Yes, simultaneous equations can have any number of variables. However, the number of equations must be equal to the number of variables in order to have a unique solution. Otherwise, there may be an infinite number of solutions or no solutions at all.

4. What are some real-world applications of simultaneous equations?

Simultaneous equations are used in various fields, such as engineering, economics, and physics. They can be used to model systems with multiple variables, such as electrical circuits, chemical reactions, or supply and demand in a market.

5. How accurate are solutions to simultaneous equations?

The accuracy of the solutions to simultaneous equations depends on the accuracy of the data and the method used to solve them. In some cases, rounding errors or approximations may result in slightly different solutions. However, with proper techniques and precise data, the solutions can be highly accurate.

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