SOLUTION: Please help me with this problem Solve the system by addition method Eq 1 states: 3x + 3y = 33 Eq 2 states: 5x - 2y = 27 I appreciate any help you can give me

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Question 102774This question is from textbook
: Please help me with this problem
Solve the system by addition method
Eq 1 states: 3x + 3y = 33
Eq 2 states: 5x - 2y = 27
I appreciate any help you can give me This question is from textbook

Answer by doukungfoo(195) (Show Source):
You can put this solution on YOUR website!
The objective when using the addition method is to eliminate one of the variables in the system of equations.
The first equation has a postive 3y
and the second has a negative 2y
so the y variable is the one we will eliminate.
but before we can do this we have to get y's coefficients to equal one another.
to do this we will multiply the first equation by 2
and then multiply the second equation by 3
so lets do that
3x + 3y = 33
multiply each term by 2
2(3x) + 2(3y) = 2(33)
6x + 6y = 66
now lets take the second equation and multiply each term by 3
5x - 2y = 27
3(5x) - 3(2y) = 3(27)
15x - 6y = 81
ok so now our system of equations looks like this
6x + 6y = 66
15x - 6y = 81
now we are ready to use the addition method
6x + 15x = 21x
6y + (-6y) = 0
66 + 81 = 147
that leaves us with
21x = 147
solve for x
21x/21 = 147/21
x = 7
So now the we have found x = 7
we can use this value for x in either of the original equations to solve for y
3x + 3y = 33
3(7) + 3y = 33
21 + 3y = 33
21 - 21 + 3y = 33 - 21
3y = 12
3y/3 = 12/3
y = 4
Answer: So our solution is x = 7 and y = 4
Check solutions by seeing if they satisfy both original equations:
3x + 3y = 33
3(7) + 3(4) = 33
21 + 12 = 33
33 = 33
AND
5x - 2y = 27
5(7) - 2(4) = 27
35 - 8 = 27
27 = 27
They both work so we know we have solved the system of equations correctly and we use the addition method to do it.