solve please: {x+y=3 {y=2x?

Question

and please show work thank you

Answer 1

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

equation 2 insert the y value into equation 1

- - - - - - - - -

x + y = 3

x + 2x = 3

3x = 3

3x/3 = 3/3

x = 1

The answer is x = 1

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - - -

x + y = 3

1 + y = 3

1 + y - 1 = 3 - 1

y = 2

The answer is y = 2

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - -

Check equation 1

x + y = 3

1 + 2 + 3

3 = 3

- - - - - - - - -

Check equation 2

y = 2x

2 = 2(1)

2 = 2

- - - - - - - - -

The solutiopn set is { 1, 2 }

- - - - - - - -s-

Answer 2

X=1 y=2

Answer 3

x=1

Answer 4

1) x+y = 3
2) y = 2x
------------
METHOD: SUBSTITUTION
The simplest way to do it here, is to solve by using equation marked with 2), then solve it for x, and use this solution to solve for y:

First, let solve it for x:
use 2) and substitute y in 1) with 2x
you get:
(1) x + 2x = 3
3x = 3 /:3 (divide both sides with 3)
x = 1

Now let's get back to equation 2):
use solution for x and include it in 2):
y = 2x
y = 2 * 1
y = 2

so, now you have it:
x = 1
y = 2

System checkup - include solutions for x and y into initial equations (1) and (2): if we did everything OK, left and right side should be equal, for each equation.
Here it goes:

(1) x +y = 3, x =1, y = 2
1 + 2 = 3
3 = 3 => OK!
(we proved system works for 1st equation)

(2) y = 2x, x = 1, y = 2
2 = 2*1
2 = 2 => OK!
(we proved system works for 2nd equation)

We proved system works for all equations in the problem, therefore our solutions for x and y are correct, and you solved the problem!
P.S. With only 2 equations in the system, you don't have to mark them (e.g. with 1) and 2), as I did) - I have marked it for you to better understand what are we doing, and with what.

Answer 5

that's easy: x+2y=x+(2x)=3 (substitution)
3x=3 -> x=3/3=1
y=2x=2*1=2

Answer 6

well you can take the second equation and substitute it for y in the first equation.

so, x+2x = 3

which then equals:

3x = 3

which means that x=1.

then using any of the two equations, you can solve for y:

1+ y = 3
y = 2

or

y = 2(1)
y = 2

thats the answer!

Answer 7

x+y=3 y=2x
x+2x=3
3x=3
3x/3=x 3/3=1

x=1

Answer 8

x+2x =3
3x =3
x=1
y=2x =2 1
y=2

Answer 9

x+y=3 y=2x

x+ (2x) =3

3x=3

x=1

Answer 10

x+y=3
x+(2x)=3 substitute 2x in for y
3x=3
x=1

y=2x
y=2*1
y=2