It does, thanks.
I'm currently working on solving algebraic equations with two variables (Example: 3x+4y=9). The computer lesson has taught me nothing but to solve the equation by trial and error -- selecting the proper ordered pair from a multiple choice list after plugging it in to see if it's correct. So, what happens when I don't have a convenient little list of ordered pairs to plug in? Is there a way to solve it from scratch like a one-variable equation?
There is a way to solve this problem from scratch.
You first find a value for either X or Y and then plug that instead of X or Y and solve for the other one.
3X + 4Y = 9
3X = 9 - 4Y
X = (9-4Y)/3
Now plug that instead of X to make it a one variable equation.
3[(9-4Y)/3) + 4Y = 9
That should result as Y=1
Than, plug 1 instead of Y to get X.
3X + 4(1)=9
that should result as X = 5/3
Than, plug the number for both X and Y.
3(5/3) + 4(1)=9
9=9
Hope it helps.
To solve algebraic equations with two variables from scratch, you can use a method called substitution or elimination.
1. Substitution Method:
- Choose one of the equations and solve it for one variable in terms of the other variable. In your example, you solved the first equation for X in terms of Y.
- Substitute the expression you found for that variable into the other equation. This will give you an equation with only one variable.
- Solve the resulting one-variable equation to find the value of that variable.
- Substitute the value you found back into one of the original equations and solve for the other variable.
2. Elimination Method:
- Multiply one or both equations by suitable numbers so that the coefficients of either X or Y in the two equations become the same or additive inverses.
- Add or subtract the equations to eliminate one of the variables and get an equation with only one variable.
- Solve the resulting one-variable equation to find the value of that variable.
- Substitute the value you found back into one of the original equations and solve for the other variable.
Both methods work effectively to solve systems of equations with two variables. You can choose the method that seems easier or more suitable for the specific problem at hand. Remember to check your solutions by substituting them back into the original equations to ensure they are valid.
To solve algebraic equations with two variables, such as 3x + 4y = 9, you can use the method of substitution. Here's a step-by-step guide on how to solve it from scratch:
1. Choose one of the equations and solve it for one variable in terms of the other variable. Let's solve for x in terms of y:
3x + 4y = 9
3x = 9 - 4y
x = (9 - 4y)/3
2. Substitute the expression you found for x into the other equation. So, substitute (9 - 4y)/3 for x in the equation: 3x + 4y = 9.
3((9 - 4y)/3) + 4y = 9
3. Simplify the equation by distributing and simplifying:
(9 - 4y) + 4y = 9
9 - 4y + 4y = 9
9 = 9
4. This equation is true, which means that any value of y will satisfy it. The equation has infinitely many solutions, represented by all possible ordered pairs (x, y).
5. If you want to find a specific solution, choose a value for y and then solve for x. Let's choose y = 1:
x = (9 - 4(1))/3
x = 5/3
6. So, one possible solution to the equation is (5/3, 1).
Remember, since there are infinitely many solutions, you can choose different values for y and get different solutions. To find additional solutions, repeat steps 5 and 6 using different values for y.