SOLUTION: i cant figure out how to get "X" and "Y"... 4x + 6y = 38 10x + 8Y = 60 they have steps but i dont understand them, please help

Question 175233: i cant figure out how to get "X" and "Y"...
4x + 6y = 38
10x + 8Y = 60
they have steps but i dont understand them, please help
Found 2 solutions by gonzo, monika_p:
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
you have 2 equations in 2 unknowns.
you need to eliminate one of the unknowns so you can solve for the remaining one.
you do this by manipulating the equations so that when you add or subtract one equation from the other, the second unknown disappears.
---
here's how it's done.
your equations are:
4x + 6y = 38
10x + 8y = 60
---
if you multiply the first equation by 10, and you multiply the second equation by 4, you will be able to eliminate the x as follows:
---
first equation:
4x + 6y = 38
multiply both sides of the equation by 10 to get:
40x + 60y = 380
---
second equation:
10x + 8y = 60
multiply both sides of the equation by 4 to get:
40x + 32y = 240
---
your two equations are now:
40x + 60y = 380
40x + 32y = 240
---
subtract the second equation from the first to get:
0x + 28y = 140
which becomes:
28y = 140
divide both sides of this equation by 28 to get:
y = 5
---
now that you have solved for y, you can substitute in either equation to find x.
go back to your original equations:
4x + 6y = 38
10x + 8y = 60
---
take the second equation and substitute 5 for y to get:
10x + 8*5 = 60 which becomes 10x + 40 = 60
subtract 40 from both sides to get:
10x = 20
divide both sides by 10 to get:
x = 2
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you should now have your answer:
x = 2
y = 5
---
to prove, substitute for x and y in the first equation:
4x + 6y = 38
4*2 + 6*5 = 38
8 + 30 = 38
38 = 38
values for x and y are good.
---
since you used the second equation to find x, you don't need to check that equation again, but we'll do it anyway to show you.
10x + 8y = 60
10*2 + 8*5 = 60
20 + 40 = 60
60 = 60
values for x and y are good.
---
you could have eliminated the y and solved for x first. i just eliminated the x and solved for y first. either way would have worked.

Answer by monika_p(71) (Show Source): You can put this solution on YOUR website!
one of the method to solve system of equation is method of elimination.
4x+6y=38
10x+8y=60
lets eliminate x, to do so you have to multiply both equations first by 10 and second by -4 then you will get
40x+60y=380
-40x-32y=-240
as you see you got 40x in first equation and -40x in second - opposits, after adding first equation to the second x will be eliminated:
40x-40x+60y-32y=380-240
28y=140 / divide both sides by 28
y=5
to find x substitute y=5 in either first or second equation
4x+6*5=38
4x+30=38
4x=8
x=2

If you want eliminate y you will get same results:
4x+6y=38/*8
10x+8y=60/*-6
32x+48y=304
-60x-48y=-360
------------------
-28x=-56 / divide by -28
x=2
then 10*2+8y=60
8y=60-20
8y=40
y=5
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