Solve the system of equations 3r - 4s = 0 and 2r + 5s = 23.

Solution:

Given, the equations are

3r - 4s = 0 and 2r + 5s = 23

⇒ 3r = 4s

⇒ r = (4/3)s --- (1)

2r + 5s = 23 --- (2)

Substituting the value of r from (1) in (2),

⇒ 2(4s/3) + 5s = 23

⇒ 8s/3 + 5s = 23

⇒ (8s + 15s)/3 = 23

⇒ 23s = 69

⇒ s = 69/23

⇒ s = 3

Now, put the value of s in (1),

⇒ r = (4/3)(3)

⇒ r = 4

Therefore, the solutions are r = 4 and s = 3.

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Solve the system of equations 3r - 4s = 0 and 2r + 5s = 23.

Summary:

The solutions to the system of equations 3r - 4s = 0 and 2r + 5s = 23 are r = 4 and s = 3.