What is the answer to 3y + 5x = 20 and 5y + 3x = 20?

Question

Solve using elimination or substitution method.

Answer 1

Substitution method :

The standard form of the equations are 5x + 3y =20 -(1) and 3x + 5y = 20 -(2)

Substitute 20 = 3x + 5y in the first equation 5x + 3y =20

5x + 3y = 3 x+ 5y

Subtract 3x from each side

5x -3x + 3y =3x - 3x +5y

2x + 3y = 5y

Subtract 3y from each side

2x + 3y - 3y = 5y - 3y

Therefore 2x = 2y

Divide each side by 2

x = y

Substitute x = y in the first equation 5x + 3y =20

Therefore 5x +3x = 20

8x = 20

Divide each side by 8

8x / 8 = 20 / 8

x = 5 / 2

Therefore y =5 / 2

The answer is x =5 / 2 and y = 5 / 2.

Answer 2

Multiply the equation 1 by 5
15y + 25x = 100 ----------- (3)

multiply the equation 2 by 3
15y + 9x = 60 ---------- (4)

subtract equation 4 from 3.
15y + 25x = 100
15y + 9x = 60
---------------------------
16x = 40
divide each side by 16
x = 40/16 = 5/2

substitute x = 5/2 in equation 1
3y + 5 * 5/2 = 20
3y = 20 - 25/2 = 15/2
divide each side by 3
y = 5/2

(x, y) = (5/2, 5/2)