Ineed when it comes to the elimation method, when one of the equations is in y=mx+b. for example.
9x+5y=44
5x-4y=51

x = 431/61; y = -239/61

Step-by-step explanation:

You need to add the two equations to eliminate one variable. If you add the equations as they are now, you will get 14x + y = 95, and as you can see, you still have two variables. You must make the coefficients of one of the variables additive inverses. That way, when you add the equations, one variable will be eliminated since its coefficients add to zero.

Let's work on eliminating y.

The first equation has 5y, and the second equation has -4y. If we multiply both sides of the first equation by 4, the y-term will become 20y. If we multiply both sides of the second equation by 5, the y-term of the second equation becomes -20y. The terms 20y and -20y will add to 0, and the y variable will be eliminated.

9x+5y=44

5x-4y=51

1) Multiply the both sides of the first equation by 4:

36x + 20y = 176

2) Multiply both sides of the second equation by 5:

25x - 20y = 255

3) Now add the equations:

61x + 0y = 431

61x = 431

Divide both sides by 61:

x = 431/61

Now that we know x, we can substitute y into one of the equations and solve for y. We can also start with the two original equations and do the appropriate multiplications and addition to eliminate x and solve for y.

I'll do elimination of x now, so you see elimination being used again.

Start with the original system again.

9x+5y=44

5x-4y=51

Multiply both sides of the first equation by -5. Multiply both sides of the second equation by 9.

-45x - 25y = -220

45x - 36y = 459

Now add the new equations.

0x - 61y = 239

-61y = 239

Divide both sides by -61:

y = -239/61

Solution: x = 431/61; y = -239/61

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