solve using elimination 2x-y=1 x+2y=4?

2x - y = 1

x +2y = 4

<=>

2x - y = 1

2x + 4y = 8

<=>

5y = 7

<=>

y= 7/5

and

x = (1 + y) / 2 =

(1 + 7/5) / 2 =

6/5


Answer :

x = 6/5

and

y = 7/5

*******

4 x - 2 y = 2
x + 2 y = 4------ADD

5 x = 6
x = 6/5

y = 2 x - 1
y = 12/5 - 1
y = 7/5

x = 6/5 , y = 7/5

x + 2y = 4
x = 4 - 2y

2x - y = 1
2 (4 - 2y) - y = 1
8 - 4y - y = 1
8 - 5y = 1
-5y = 1
y = -1/5

x + 2y = 4
x + 2 (-1/5) = 4
x - 2/5 = 4
5x - 2 = 20
5x = 22
x = 22/5
x = 4 2/5

The answer is (4 2/5, -1/5), blasy.

2x - y = 1 --- (1)
x + 2y = 4 --- (2)

(1) x 2 : 2(2x - y) = 2 x 1 = 2
4x - 2y = 2 --- (3)
(2) + (3) : (x + 2y) + (4x - 2y) = 4 + 2
x + 2y + 4x - 2y = 6
x + 4x + 2y - 2y = 6
5x = 6
x = 6/5 = 1.2

Sub x = 1.2 into (1) :
2x - y = 1
2(1.2) - y = 1
2.4 - y = 1
-y = 1 - 2.4 = -1.4
y = 1.4

Multiply x+2y+4 on both sides by -2,
giving you -2x-4y=-8.
So adding both equations, you get
-5y=-7, so
y=-7/-5=7/5.

So, you figure out x now.

2x - y = 1
x + 2y = 4

x + 2y = 4
2(x + 2y) = 2(4)
2x + 4y = 8

....2x - ..y..= 1
‒) 2x + 4y = 8
------------------------------
..........-5y = -7

-5y = -7
y = -7/-5
y = 7/5 (1.4)

2x - y = 1
2x - 7/5 = 1
2x = 5/5 + 7/5
x = (12/5)/2
x = (12/5)(1/2)
x = 6/5 (1.2)

∴ x = 6/5 (1.2), y = 7/5 (1.4)

2x-y=1 ==> y=2x-1

x+2y=4 ==> x+2(2x-1)=4
==> 5x-2=4
==> x=6/5
y=2x-1=7/5

3x+2=5