How to solve for 2x + y = 50, must find both x and y?

Question

I have a faint idea on how to go about it but I keep coming to a dead end... 2x + y = 50 orignated from 3x + y = 65 and x + y = 35. Correct me if I did anything wrong.

EDIT: I want to solve for both x and y. I can guess and get it right, but I have to show work the process at which I arrived at my answer, and I cannot say I used guess and check, so someone please help me!

Answer 1

you made a mistake i think. you can't solve one equation with two variables.

but, if the two original equations were x+y = 35 and 3x + y = 65 then it isn't too hard

step 1: y = 35 - x
step 2: insert the above into the second equation so ...
3x + (35 - x) = 65
step 3: solve for x
2x + 35 = 65
2x = 30
x = 15
step 3: insert x=15 into the original equation x + y = 35
15 + y = 35
y = 20

or you can subtract the two equations

step 1:
3x + y = 65
-(x + y) = - 35
-------------------

which is

3x + y = 65
- x - y = -35
-----------------
2x + 0y = 30
which is the same as
2x = 30
x = 15

step 3: insert x=15 into the original equation x + y = 35
15 + y = 35
y = 20


hope that helps

Answer 2

OK if x+y = 35
and 2x+y = 50
and 3x+y = 65
then you know the value of x straight away, it's 15 because all you're doing is adding x to the equation each time and the total is going up by 15
so if x=15, and x+y=35, then y must =35-15=20

so x=15, and y=20

Answer 3

Where did that 2x+y=50 come from?

The solution to 3x+y= 65 and x+y= 35 is:
3x+y=65 (a)
x+y=35 (b)
First take (a)
3x+y=65
y=65-3x
Now replace "y" in (b)
x+(65-3x)=35
x+65-3x=35
x-3x=35-65
-2x=-30
30=2x
30/2=x
x=15

If you want to find "y" Just replace "x" whether in (a) or in (b)
3x+y=65 (a)
3(15)+y=65
45+y=65
y=65-45
y=20

x+y=35 (b)
15+y=35
y=35-15
y=20
Please, let me know if you need more help with this.

Answer 4

discover the point the position the line meets the circle through rearranging the equation of the line: 7x-y-2=0 y = 7x - 2 replace into the circle equation: x^2+(7x-2)^2-9x-9(7x-2)+28=0 x^2+49x^2-28x+4-9x-63x+18+28=0 50x^2-100x+50=0 Divide for the time of through 50: x^2-2x+a million=0 Factorise: (x-a million)^2 = 0 giving the x fee of one million replace back into the line equation to discover the y fee: 7 - y - 2 = 0 y = 5 So the line and the circle meet at (a million,5) and no different factors. Any line which meets a circle at a unmarried element ought to through definition be tangent to the circle.

Answer 5

Okay, we start off like this:
Since you've got 3 equations make use of the easy ones.
x+y=35 ---- Call this eq.1
2x+y=50 ---- Call this eq.2
3x+y=65 ---- Call this eq. 3

Take eq.2-eq.1, then you'll wind up with x=15
Substitute x=15 into eq.1, and you'll get y=20

=P

Answer 6

x+y=35
3x+y=65
y=35-x

3x+ 35-x=65
2x+35-35=65-35
2x=30
x=15
15+y=35
15-15+y=35-15
y=20

Answer 7

x = -y +35

3(-y + 35) + y = 65

-3y + 105 +y = 65

-2y = -40

y = 20

___________________

x + y = 35

x + (20) = 35

x = 15