I help with Algebra 1?

Question

I need help with Elimination by solving the System of Equations. Can someone explain to me how Elimination using Multiplication works? I have a quiz on it tommorow. Show the work too please:
1) 1.8x-0.3y=14.41
x-0.6y=2.8

2)3x-1/2y=10
5x+1/4y=8


3)3x-4y= -10
5x+8y=-2

Answer 1

To eliminate, multiply one equation by a constant until the coefficients of a variable match, then add the equations to eliminate it, hence the name.

Taking the third one as an example, you can multiply the first equation by 2 to get 6x - 8y = -20
Then, adding the two equations gives (6 + 5)x + (8 - 8)y = -20 + -2
which simplifies to 11x = -22
Therefore, x = -2, which you can put back into either equation (I'll pick the second) to get 5(-2) + 8y = -2
8y = -2 + 10
y = 1

The others work on the same principle: multiply one equation by a constant to get the coefficients to match, then add/subtract.

Answer 2

In systems of equations, you want to line up like terms so that when you add the equations, you can cancel out a variable. To give a simplified example, let's look at x + y = 3 and x - 2y = 9:

1x + 1y = 3
1x - 2y = 9

If we added top to bottom, we'd get 2x and -y... but what if we multiplied the entire top equation by 2?

2(1x + 1y = 3) = 2x + 2y = 6, now we have:

2x + 2y = 6
1x - 2y = 9
------------------
3x + 0y = 15

3x = 15
3x/3 = 15/3
x = 5

Then we substitute 5 for x in any of the equations to solve for y:

x + y = 3
5 + y = 3
y = -2

That is how systems of equations work.

So if we look at your equations, we try to find something we can multiply one of the equations by to get one of the variables to add to 0.

1) we can do this a number of ways, but let's multiply the first equation by -2:

-2(1.8x - 0.3y = 14.41) = -3.6x + 0.6 y = -28.82

-3.6x + 0.6y = -28.82
1x - 0.6y = 2.8
------------------------------
-2.6x + 0y = -26.02
x = 10.015

You should finish this one and do the other two to practice for your quiz tomorrow.

Best of luck! :)

Answer 3

1) (1.8x- 0.3y =14.41)1 {multipy each equation to be
( x- 0.6y = 2.8)-1.8 able to cancel out the x's}
---------------------------------
1.8x- 0.3y =14.41 {solve}
-1.8x+0.54y= -5.04
--------------------------------
0.24y= 9.37 {divide to get y by itself}
------ ------
0.24 0.24
y= 39.04(rounded)

x -0.6(39.04)=14.41 {plug y into original equation,
doesn't matter which one it is}
x- 23.424=14.41
+23.424 +23.424 {add to get x by itself}
x=37.834

so x=37.834 and y =39.04(rounded)

use this one as examples for rest.

Answer 4

i am sorry but i almost failed that part of math...just do what i did...go and see your teacher and ask a bunch of questions untill you understand it completly

Answer 5

Try asking your good friends for help?

Answer 6

wait, i know this doesn't really answer your question, but why don't you just look in your notes?