# solve for x and y: 2x-y = 5 x+y = 3

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2x - y = 5 ...... (1)

x + y = 3 ........(2)

We will use the elimination method:

Add (1) and (2):

==> 3x = 8

**==> x= 8/3**

Now to calculate y, we will substitute in (1):

2x -y = 5

==> y= 2x-5 = 2(8/3) -5 = 16/3 -5 = (16-15)/3 = 1/3

==> **y= 1/3**

Take the two equations:

2x - y = 5

x + y = 3

Add the two equations:

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

=> 3x = 8

=> x = 8 / 3

Substitute x = 8 / 3 in x + y =3.

=> (8 / 3) + y = 3

=> y = 3 - (8 / 3)

=> y = (9 - 8) / 3

=> y = 1 /3

**Therefore x= 8 / 3 and y = 1 / 3.**

2x-y = 5

x+y = 3

to find out x add the equations together

so

2x-y = 5

+ x+y = 3

3x=8

x=8/3

so

8/3+y=3 so

y= 1/3

2x - y = 5

x + y = 3

First cancel out the " y " by adding. Which means you have to add 2x with " x " too.

By adding, your equation would look like

**3x = 8 **now divide both sides by 3

By dividing, your equation should look like

**x = 8/3 **which is the answer for " x "

Now plug 8/3 into one of the equation

**8/3 + y = 3 **subtract both sides by 8/3

By subtracting your equation would look like

**y = 1/3 **which is your answer for " y "

So your answer is **x = 8/3 ; y = 1/3**

(a) 2x-y = 5

(b) x+y = 3

I am going to use the method called elimination.

Add the two equations together:

2x - y = 5

+ x + y = 3

_____________

3x = 8

Solve for x:

x = 8/3

Rearrange equation (b) for y:

x + y = 3

y = 3 - x

Plug in known value of x:

y = 3 - (8/3) = 1/3

x+y=3

x+y-y=3-y

x=3-y

2x-y=5

2(3-y)-y=5

6-2y-y=5

6-2y-y-6=5-6

-2y-y=-1

-3y=-1

-3y/-3=-1/-3

y=1/3

x+y=3

x+1/3=3

x+1/3-1/3=3-1/3

x=8/3

So y=1/3 and x=8/3

**We'll solve the system of equations:**

2x-y = 5 (1)

x+y = 3 (2)

We'll solve the system using the substitution method.

We'll subtract y both sides, in the second equation:

x = 3-y

We'll subtract 3 both sides:

x-3 = -y (3)

We'll substitute (3) in (1):

2x-y = 5

2x + x - 3 = 5

We'll combine like terms:

3x - 3 = 5

We'll add 3 both sides:

3x = 5+3

3x = 8

We'll divide by 3 both sides:

**x = 8/3**

We'll substitute x in (3), to find out the value of y:

x-3 = -y

8/3 - 3 = -y

We'll multiply -3 by 3:

(8-9)/3 = -y

-1/3 = -y

We'll multiply by -1 both sides:

**y = 1/3**

**The solution of the system of equations is {(8/3 , 1/3)}.**

2x-y = 5.... (1)

x+y =3...(2)

To solve for x and y.

From (1) we get 2x-5 = y. So substitute for y by 2x-5 in equation (2):

x+2x-5 =3

3x-5 = 3

3x = 5+3 = 8

x = 8/3.

Now from eq (2), x+y = 5.

8/3 +y = 5

y = 5-8/3 = (15-8)/3 = 7/3

Therefore x= 8/3 and y = 7/3