Simultaneou Equation?

Question

Hi.

Could anyone list several websites regarding the soving of simultaneous equations using the elmination method.Here is an example:

3x+2y=8
x-3y=-23

And could some show a precise working to solve such questions and list some examples. Your assistance will be greately appreciated.Thank you

Answer 1

You want to add or subtract these equation so that either the x-values add up to zero or the y-values add up to zero. In this case, neither one will add to zero in their present form...

So, multiply the second equation by -3. Why? Because the coefficient of x in the first equation is positive 3. If we have opposite values of coefficients for x, then the x-values will have a sum of zero.

3x + 2y = 8
x - 3y = -23

3x + 2y = 8
-3[x - 3y = -23]

3x+2y=8
-3x + 9y= 69

Add the equations
(add x's to x's, y's to y's, and constants to constants)

11y = 77
y = 7

Substitute this value into any equation with an x and y.

3x + 2(7) = 8
3x + 14 = 8
3x = -6
x = -2

The solution is ( -2 , 7 )

Answer 2

Not sure what level you're working at, so here goes. This method should be called the elimination/addition method. The idea is to add the two equations together vertically, BUT only if in doing so, one of the two variables is eliminated in the resulting equation. You can multiply either equation by any constant, so here, you could eliminate x by multiplying the bottom equation by -3. Be sure to multiply ALL the terms in the equation by this value. You should get -3x+9y=69. Now, if you add this new equation to the original top equation, 3x+2y=8, the variable x is eliminated. Yay! You should get a simple equation in y, easy to solve. Once you know the value of y, substitute it into either original equation, and you can find the value of x.
You could also eliminate y, but it would require you to multiply both original equations by different numbers, so that the resulting equations have y-terms that have the same coefficient, but opposite sign. Here, you can make 6y and -6y easily. Multiply the top equation through by 3, and the bottom one through by 2 (remember to multiply both sides of each equation). Now, when you add the two new equations together, y is eliminated, and you have a simple equation in x to solve. Once you know the value of x, substitute that into any original equation to get the value of y.
What solution did you get?
Try this page: http://www.mathpower.com/tut336.htm
Or this one (you may not need 3 equations in 3 variables, but there's a nice explanation of 2 equations in 2 variables given first:
http://mathforum.org/library/drmath/view/66009.html

Answer 3

3 times 2 plus 2 times 1=8
get it
3*2+2*1=8

4 minus 3 times 23
4-3*23

i can't explain
and i didn't find any websites including equation activities

Answer 4

9x + 6y = 24
2x - 6y = - 46-----ADD
11x = - 22
x = - 2
- 6 + 2y = 8
2y = 14
y = 7

x = - 2, y = 7