How do I solve a simultaneous equation?

Question

I have a maths test tomorrow, if you can explain on how to solve a simultaneous equation in the most basic form that will help a lot...thank you

Answer 1

Start with equation 1, and simplify to x= [expression]

Then, in equation 2, remove all references to x, and replace with [expression].

Then solve equation 2 normally, and you're done!

Answer 2

There are 2 ways to solving simultaneous equations.
The eliminating method and the substitution method.
I apologize for only knowing the eliminating method, because I've been using that method for all simultaneous equations.

We'll use tnova4's equation as an example.
2x + 4y = 5
4x + 6y = 0

Eliminating method

You can decide to find either x or y first, i choose to find x first. So I'll eliminate y. How? Multiply the whole equation by a number so that the value of both y(s) will be the same, but one value must be a positive and the other a negative.

2x + 4y = 5 (multiply the whole equation by 6)
We'll have 12x + 24y = 30

4x + 6y = 0 (multiply the whole equation by -4)
We'll have -16x - 24y = 0

Add both equations together and we'll have 12x - 16x + 24x - 24x = 30 + 0
Do the sums and we'll have -4x = 30
Eliminate -4 from the left hand side by dividing -4 from both sides
-4x/-4 = 30/-4
x = -7.5

Now that you have found the value of x, you can find the value of y easily.

Choose one equation from the 2 that you find it easier to solve.
I choose the 2nd equation, which is 4x + 6y = 0

Now you know x = -7.5
Replace x with -7.5 in the equation
4(-7.5) + 6y = 0
-30 + 6y = 0
Eliminate -30 by adding 30 to both sides
-30 + 30 + 6y = 0 + 30
Do your sums and you'll have 6y = 30
Now you'll have to eliminate 6 by dividing 6 from both sides.
6y/6 = 30/6
and you'll have y = 5

Your question is solved with x = -30, y = 5.

Answer 3

You can not solve "a" simultaneous equation. You must have two equations that contain only x and y as unknowns or three equations containing x, y and z as unknowns. They are simultaneous equations because the unknowns have the same numerical values at the same time which you must find!

Solve either equation (of two equations) for x = whatever, where 'whatever' includes only y and numerical constants but no x's.

Plug the result (whatever) into the second equation wherever there is an x and it will now include only y and numerical constants. Solve for y which should be a numerical value (answer one).

Plug the numerical value of y into the first equation and solve for a numerical value of x (answer two).

Think of it as a simple game with unchanging rules, despite how complex it can get. Good luck.

Answer 4

Solving System of Equations (Simultaneous Equations)

There are two Methods

Substitution Method

Elimination by addition Method

The Links will explain.

Click on the URL below for additional information concerning solving System of Equations

library.thinkquest.org/10030/10lsoeq.htm

www.as.ysu.edu/~faires/PreCalculus3/systemsofequations.pdf

- - - - - - -s-

Answer 5

You got very good explanations. I suggest you the first method.

The trick is to eliminate x (or y), so that you have only 1 equation and only 1 letter.

ie:

5x + ... = ...
7x + ... = ...

Multiply the first one by 5 and the second one by 7 (all the equation, not only the x term!!)

Then substract.

This is the same than multiplying the first one by 5 and the second one by -7. Then, you add.

When you have calculated y, then plug it in the first equation (or in the second one), and find x.

Take care

Ana

Answer 6

2x + 4y = 5
4x + 6y = 0

Multiply the top equation by 2, to make one of the terms equal:

4x + 8y = 10
4x + 6y = 0

Subtract:

2y = 10

Solve:

y = 5

Use this to solve for x:

4x + 6(5) = 0

4x = -30

x = -7.5

Answer 7

Graph them all, and see where they intersect!