3x +5y=9 and 5x +3y=7, then x+y =?
Answers
Answer:
x + y = 2
Step-by-step explanation:
3x + 5y = 9 --[eqn. 1]
5x + 3y = 7 --[eqn. 2]
Multiply equation 1 by 5 and equation 2 by 3,
5(3x + 5y) = 5(9)
15x + 25y = 45 --[eqn. 3]
3(5x + 3y) = 3(7)
15x + 9y = 21 --[eqn. 4]
Subtract equation 4 from equation 3,
15x + 25y - (15x + 9y) = 45 - 21
15x + 25y - 15x - 9y = 24
16y = 24
y = 24/16
y = 3/2 = 1.5
Substitute y = 1.5 in equation [1],
3x + 5y = 9
3x + 5(1.5) = 9
3x + 7.5 = 9
3x = 9 - 7.5
3x = 1.5
x = 1.5/3
x = 0.5
Therefore, x = 0.5 and y = 1.5
⇒ x + y = 0.5 + 1.5 = 2
Answer:
3x+5y=9 …(1)
5x+3y=7 …(2)
Let us simplify the equations by eliminating a variable
Make the coefficients of X or Y equal
Multiply equation (1) with 5 and equation (2) with 3
We get 15x+25y=45 and 15x+9y=21
Now subtract the equations, we get
(15x+25y)-(15x+9y)=(45–21)
16y=24, y= 24/16 = 3/2
Substituting the value of y in equation (1) we get
3x+5(3/2)=9
3x+15/2=9
3x=9–15/2
3x=3/2
x =1/2
x+y =3/2+1/2= 2
x+y=2
The other method is simply add equations (1) & (2)
You get
8x+8y=16
x+y=2