Solving systems of linear equations using elimination?

Question

Can you do one of these two and show me all the steps?

3x - 10y = -25

4x + 40y = 20

-or-

3x+2y = -9

-10x + 5y = - 5

These are the two hardest problems in my homework, and I need someone to solve and show their work so I can learn from it.

I'm not looking to cheat the answer off you, I really really don't understand this.

Answer 1

hey its easy i took ALE1 last year :D anyways you have to

             make "x" or "y" the same so they can be eliminated...

                3x-10y=-25

                4x+40y=20

okay the -10 can be mutilpled to =40

        4(3x-10y)=-25   which give you 12x-40y=-100

so now elimnate

               12x-40y=-100

                 4x+40y=20   the -40y and + 40y can go

             you have to subtract all the way down

              8x=-80

               you divide 8x from each side so x = -10 :D btw plug your answer back in to check again

Answer 2

With any equation, if you multiply EVERYTHING in the equation by a number, you get an equivalent [equal] equation.  For example:

4 * [3x - 10y = -25]  ->  12x - 40y = -100

These two equations are the same, and you can replace one with the other.  Note: I multiplied by 4, but you can choose any number you want.  

If I replace the top equation, the system becomes

12x - 40y = -100

4x + 40y = 20

This is weird, but we're going to add the equations together! Remember, you can only add like terms!

12x + 4x = 16x

-40y + 40y = 0y

-100 + 20 = -80

The sum of the system is

16x = -80    Since the -40y and +40y cancel each other out, the Y variable is "eliminated :)"  Since the new equation has one variable, we solve it easy style, dividing by 16 in this case.  So x = -5, but that's only half.

Now, we substitute x= -5 in any equation, and solve for y!

3*(-5) - 10y = -25

-15 - 10y = -25

-10y = -10

y = 1

4*(-5) + 40y = 20

-20 + 40y = 20

40y = 40

y = 1

12*(-5) - 40y = -100

-60 - 40y = -100

-40y = -40

y = 1

So, you can substitute into any equation, and you should get the same answer every time.  Now, the answer is x = -5, y = 1, or (-5,1).

So, you multiply one or both original equations, so that one variable has opposite coefficients.  Then you add the equations together, and one variable will be eliminated.  Solve this sum like normal, then substitute your answer into an original equation, to get the second half.  Whew!

For your second system, I would multiply the top equation by 10, and your bottom equation by 3.  Your new system should eliminate the x variable!

Answer 3

Okie Dokie

3x-10y=-25

4x+40y=20

You want to make it so that you can eliminate one of the variables

so we will divide the bottom equation by four(it will make the numbers smaller)

3x-10y=-25

1x+10y=5

now we can eliminate the y values(just for now)

add the two quations together

4x=-20

solve for x

x=-5

now you are going to plug that back into one of the equations and solve for y

3(-5)-10y=-25

-15-10y=-25

-10y=-10

y=1

now check your answers

3(-5)-10(1)=-25

-15-10=-25

-25=-25

and

4(-5)+40(1)=20

-20+40=20

20=20

Now do the other equation and see if you get it.

Your answer should be:

x=-1

y=-3