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
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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
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.
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