SOLUTION: If 2x - 3y = 0 and 3x + 2y = 13, find x + y. Do I solve for x and y and then just add them. Please show me.

Question 62413: If 2x - 3y = 0 and 3x + 2y = 13, find x + y. Do I solve for x and y and then just add them. Please show me.
Found 2 solutions by 303795, jai_kos:
Answer by 303795(602) (Show Source): You can put this solution on YOUR website!
Yes your idea is correct.
Equation 1 : 2x - 3y = 0
Equation 2 : 3x + 2y = 13
Multiply the first equation by 2 and the second equation by 3. This will give a -6y in the first equation and a 6y in the second equation which can easily be eliminated.
New Equation 1 : 4x - 6y = 0
New Equation 2 : 9x + 6y = 39
Add the two equations together to get
13x = 39
Obviously x must be 3. Substitute x=3 into one of the two equations.
2*3 - 3y = 0
6=3y ie y must be 2
Therefore x + y = 3 + 2 = 5
Answer by jai_kos(139) (Show Source): You can put this solution on YOUR website!
Consider equation(1), we get
2x - 3y = 0
2x = 3y
x = 3y / 2 --->(3)
Substitute equation(3) in equation (2), we get
3 (3y / 2) + 2y = 13
9y / 2 + 2y = 13
Mulitply by 2 throughout,we get

9y + 4y = 13 * 2
13 y = 13 * 2
y = 13 * 2 / 13
y = 2 --->(4)
Now substitue equation(4) in equation(3), we get
x = 3 * 2 / 2 = 3 --->(5)

Add equation (4) and eqaution(5)
We get x + y = 3 + 2 = 5
x +y = 5
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