## dusty 2 years ago Solve using two different methods. Explain which method you found to be more efficient. a.) 3x-9y=3 6x-3y=-24

1. dusty

2. hba

We can use two methods 1-Substitution 2-Elimination.

3. hba

@dusty Do you know how to do these methods ?

4. dusty

no i don't really. Will you explain it to me?

5. hba

Sure thing. lets take an example first.

6. hba

Elimination method: When adding two equations, you basically add all parts of them. Say you had the equations: 4x + 5y = 14 -4x - 3y = -10 Adding them would give 2y = 4 4x + 5y = 14 + -4x - 3y = -10 2y = 4 As you can see, the 4x and -4x cancelled out, therefore eliminating the variable x, leaving an equation with only one variable (y), able to be solved. 2y = 4 y = 2 Now that you have a value for y, you must find one for x. To do this, just substitute the value for y into either original equation, and solve it for x 4x + 5(2) = 14 4x + 10 = 14 4x = 4 x = 1 Your solution for these two equations is (1, 2).

7. hba

x + y = 4, and 2x + y = 7. First you work in one equation, solving for one variable in terms of another. Let's solve for y in terms of x in the first equation (you can do whichever variable in whichever equation you want, but you should experiment, and start recognizing which is the simplest one). x + y = 4 -x -x y = 4 - x Now this is where the substitution comes in. We substitute this value for y in the second equation. 2x + y = 7 2x + (4 - x) = 7 2x + 4 - x = 7 Combine like terms... x + 4 = 7 -4 -4 x = 3 Now you've solved for one variable, x, but you still need y. So...substitute your value for x into either equation and solve that linear equation to find y. x + y = 4 3 + y = 4 -3 -3 y = 1 The solution to this equation is x = 3, y = 1.

8. hba

@dusty Source:Tripod If you want a step by step solution i will solve it for you.

9. dusty

Its okay I think i get it (: thanks alot!!

10. hba

Your'e welcome.