SOLUTION: my daughter needs help with two step equations using the addition method. Can someone help her with this problem: 4x-y=1 3x+y=13

Question 63141: my daughter needs help with two step equations using the addition method. Can someone help her with this problem:
4x-y=1
3x+y=13
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
my daughter needs help with two step equations using the addition method. Can someone help her with this problem:
:
The addition method means that when you add the equations one of the unknowns
is eliminated, often you have to mult one or both equations to get this to
happen, however, in these, you will eliminate y if just add them like they are:
:
4x - y = 1
3x + y = 13
-------------- add
7x + 0 = 14; note that a +y and -y, added, is 0
:
So you have:
7x = 14
:
Divide both sides by 7 and you have:
1x = 14/7
x = 2
:
We know x, so we can find y by substituting 2 for x in the 1st equation:
4x - y = 1
4(2) - y = 1
8 - y = 1
:
Subtract 8 from both sides:
8 - 8 - y = 1 - 8
-y = -7
:
we have to have y positive, we get this by multiplying the equation by -1
y = + 7
:
Our solution is x = 2; y = 7
:
Check this by substituting for x & y in the 2nd equation:
3x + y = 13
3(2) + 7 = 13
6 + 7 = 13; proves our solutions are correct
:

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