Find X and Y, by adding: 2x + 5y =20 and -2x +5y =10?

Question

I was given the hint to add both linear equations:
2x + 5y =20
-2x + 5y = 10

and I have to find both X and Y.

I came up with:

0 + 10y = 30

so x=0 and y=3

but I plugged the numbers in and it's obviosuly wrong. Can someone please help, I feels stupid, this is probably really easy...

Answer 1

You got y right. Now plug 30 in for y in one of your oringal equations to solve for x.

2x + 5y = 20
2x +5(3) = 20
2x + 15 = 20
2x = 5
x = 5/2

Now plug in x=5/2 and y=3 in your other equation to check your work.

-2(5/2) + 5(3) =
-5 + 15 = 10

It checks out, so both your x and y are correct.

TIP: I think you got x=0 from your 0+10y=30 equation. If so, please know you can't use that for x, just for y. You got rid of the x's by adding the equations so that you could isolate y and solve for y only. Once you have y, you have to go back to one of your equations that has x in it in order to solve for x.

Answer 2

Using simultanoeus equation, addind the two equtions, we have
2x +5y = 20 ------------(1)
-2x + 5y = 10--------------(2)
---------------------
o + 10y = 30
10y= 30
y= 3
Substituting y=3 in any of the euqations, say equation (2)
we have - 2x + 5y = 10 ...........and y = 3
-2x + 5 (3) = 10
-2x + 15 =10
-2x = 10 - 15
-2x = - 5
x = 5/2
therefore, x = 5/2 and y = 3

Answer 3

(2x + 5y) + (-2x + 5y) = 20 + 10
2x + 5y - 2x + 5y = 30
5y + 5y = 30
10y = 30
y = 3

2x + 5(3) = 20
2x + 15 = 20
2x = 20 - 15
2x = 5
x = 5/2

Check the solution.
-2(5/2) + 5(3) = -5 + 15 = 10

Answer 4

2x + 5y =20
-2x + 5y = 10

0x+10y=30

y=3 x=0

2x+5y=20

2x+5*3=20
2x+15=20

2x=5
x=5/2

Answer 5

you were right about y=3. now u put that value to the first one:
2x + 5*3=20 and find that x= (20-5*3)/2= 2.5 so there the answer is: (2.5,3)

Answer 6

2x+5y=20
-2x+5y=10
If you add both equations you will get:
2x-2x+5y+5y=20+10
10y=30
y=3

Than you substitute with the value of y=3
2x+3*5=20
2x=20-15
2x=5
x=2.5

Answer 7

y = 3
but x is not 0

2x+5y = 20
2x= 20-15
x= 2.5

Answer 8

2x+5y=20.....1
-2x+5y=10.....2
Adding eqns. 1&2
10y=30
y=3
Substitute in eqn.1
2x+5*3=20
2x=5
x=2.5
Verify
Substitute x,y values in eqn.2
-2*2.5+5*3
=-5+15
=10
ok

Answer 9

hey y=3 ,,,thats right...
BUT x doenst = 0 ...u just assumed that..

when y=3
then, 2x + 5*3 = 20
x=2.5

Answer 10

y is equal to 3... that part is correct I can see at a glance, but you need to substitute 3 for y in the original equations. If you do that, you'll see that x=2.5