Need Help Please. finding values of x and y in this equation?

Question

How do you find the values of x and y?
100 = 6x+7y. where x+y=15?

I know the answers, but can't do the figuring. I need to apply this formula to other equations and need to know how to "do the work". Thanks in advance!

Answer 1

x+y=15
or,x=15-y.......(eqn 1)
6x+7y=100
or,6(15-y)+7y=100
or,90-6y+7y=100
or y=100-90=10
Plugging y in eqn 1,we get
x=15-10=5
x=5 and y=10 ans

Answer 2

100=6x+7y --- (1)
x+y=15 --- (2)
from (2) y=15-x
(1) becomes 100=6x+7(15-x)
100=6x+105-7x
100=-x+105
add x to both sides
100+x=-x+x+105
100+x=105
subtract 100 from both sides
100-100+x=105-100
x=5
using (2) 5+y=15
y=10
x=5, y=10

check: 100=6x+7y --- (1)
100 = 6(5)+7(10)=30+70

Answer 3

There are a few ways of doing this problem. I will show you the "substitution" method. First, determine which eqn is simplest to solve for a variable:

Solve the 2nd eqn for x:

x = 15 - y

Now substitute in the 1st eqn:

100 = 6(15-y)+7y
100=90-6y+7y
10=y

Now substitute back in to 2nd eqn:

x+10=15

x=5
--------------------------
The other way is the "elimination" method. Here, you will manipulate one eqn to eliminate a variable when you add the two eqns together:

Multiply the 2nd eqn by -6:
-6x - 6y = -90

Now add the two eqns:

-6x-6y=-90
+6x+7y=100
----------------
y = 10

(Notice how the "x" variable cancels)

Now substitute the y-value in to the simplest eqn:

x + 10 = 15

x = 5.

Answer 4

100=6x+7y , x+y=15
100=6x+7(15-x)
100=6x+105-7x
x=5
y=15-5
y=10

Answer 5

y = 15 - x

100 = 6x + 7(15 - x)
100 = 6x + 105 - 7x
x = 5
y = 10