solve the following system of equations by addition method. x +5y=10 -2-10y=-20?

Answer 1

x +5y=10-----------------------1
-2-10y=-20---------------------2

Using addition method!
Solve for y in 2 then plug back to 1 is one way.

If we take a look at the equations, we say okay, we want to add y components, but they dont have the same coefficient.
Lets make one, and later I will explain why we want to make the same coefficient.

We times the first equation by 2.
x +5y=10 times 2

2x + 10y = 20

We list them together again,
2x + 10y = 20---------------3
-2-10y=-20-------------------4

We add 3 and 4

2x -2 = 0

2x -2 + 2 = 0 + 2

2x = 2

2/2x = 2/2

x = 1

how about y?
we can either plug into equation 1 or solve by equation 2 alone.

If we plug into 1, we will have:
x +5y=10-----------------------1

1 + 5y = 10

1 -1 + 5y = 10 -1

5y = 9

5/5 y = 9/5

y = 9/5

If we solve y by using only equation 2:
-2-10y=-20--------------------- 2

-2 + 2 -10y = -20 + 2

-10y = -18

-10/-10 y = -18/-10

y = 18/10 = 9/5

See how we solve the y in two ways?

Now we combine the answers,

x = 1
y= 9/5

~~~~~~~~~~~~~~~~~~~~
Thinking!!!
So we solved it, but why did we need to get the same coefficient? Its easier to do the problem because if you just add 1 and 2 you will get
x +5y=10-----------------------1
-2-10y=-20---------------------2

x -2 -5y = -10

But this equation is more complicated than the one we got. It contains x, y and number part.

There fore, getting rid of one variable in a system is crucial and important!

Answer:
x = 1
y= 9/5


* still confused? write back

Answer 2

x + 5y = 10
-2 - 10y = 20

let's solve for y, then use substitution.

-2 - 10y = 20
add 2 to both sides

- 10y = 22
isolate y by dividing -10 to both sides

y = -22/10 = - 11/5

now substitute:
x + 5y = 10
x + 5(-11/5) = 10
x +1(-11) = 10 NOTE: 5 cancels out
x - 11 = 10
add 11 to both sides
x = 21

CHECK:

x + 5y = 10
21 + 5(-11/5) = 10
21 - 11 = 10

-2 - 10y = 20
-2 - 10(-11/5) = 20
- 2 - 2(-11) = 20
-2 + 20 = 20

Answer 3

x + 5y = 10
-2x -10y = 20 <===== I'm assuming that you missed the x here

x + 5y = 10 <==== multiply both sides by 2 (Why? see below)
-2x -10y = 20

2x + 10y = 20
-2x -10y = 20 <========== add them together
---------------------
0 + 0 = 40

0 = 40 ????!!!!????
Well, when you get a bogus result like this, there is NO SOLUTION. That means there are no pairs of numbers (x, y) that will solve both equations.

**** I multiplied both sides by 2 because that gave me a coefficient on x of "2" on the first equation and "-2" Then, the sum will equal 0x -- thus, eliminating x from the system.

Answer 4

Should question be:-
x + 5y = 10
- x - 10y = - 20-----ADD
- 5y = - 10
y = 2

x + 10 = 10
x = 0

x = 0 , y = 2

Answer 5

(x+5y=10)x2 -2-10y=-20 = -10y=-18
= 2x+10y=20
+
-10y=-18
2x=2
x=1

Sub x=1 into x+5y=10
1+5y=10
5y=9
y=9/5

Answer: y=9/5, x=1

Answer 6

- 2 - 10y = - 20
10y = 18
y = 9/5

x + 5(9/5) = 10
x + 9 = 10
x = 1

Answer: x = 1, y = 9/5 or 1 4/5

Proofs:
1 + 5(9/5) = 10
1 + 9 = 10

- 2 - 10(9/5) = - 20
- 2 - 18 = - 20

Answer 7

First solve 10-2-10y=-20
8-10y=-20
-8 on both sides
-10y=-28
divide by -10 on both sides
y=2.8

Now if x+5y =-20 and y=2.8
x+5(2.8)=-20
x+14=-20
subtract 14 on both sides
x=-34

So x=-34, y=2.8