Solve 5x - 6y = -38 and 3x + 4y = 0
(4, 3), (-4, 3), (4, -3), (-4, -3)

Solution:

Given:

Two equations are 5x - 6y = -38 and 3x + 4y = 0

The equations are in the form of ax + by + c = 0

In order to solve, we need to make the coefficients equal to that one arbitrary constant gets cancelled.

Let 5x - 6y = -38 --- (1)

and 3x + 4y = 0 --- (2)

Multiply equation (1) with 3, we get

⇒ 3(5x - 6y) = -38

⇒ 15x - 18y = -114 --- (3)

Multiply equation (2) with 5, we get 5(3x + 4y ) = 0

⇒ 15x + 20y = 0 --- (4)

Now,

Subtract (4) from (3)

We get, -38y = -114

⇒ 38y = 114

⇒ y = 114/38

⇒ y = 3

Put y = 3 in eq (2), we get

⇒ 3x + 4y = 0

⇒ 3x + 4(3) = 0

⇒ 3x = -12

⇒ x = -4

The solution set for the given equations 5x - 6y = -38 and 3x + 4y = 0 is (-4, 3).

---

Solve 5x - 6y = -38 and 3x + 4y = 0

Summary:

By solving 5x - 6y = -38 and 3x + 4y = 0, we get x = -4 and y = 3.