(4 3) 4x-5y=30

3 min read Jun 16, 2024

Solving for x and y in the Equation 4x - 5y = 30

This article will guide you through the process of solving for x and y in the linear equation 4x - 5y = 30.

Understanding the Equation

The equation 4x - 5y = 30 represents a straight line. To find the values of x and y that satisfy this equation, we need to find the points on this line.

Solving for x

To solve for x, we can isolate it in the equation. Here's how:

Add 5y to both sides of the equation:
```
4x - 5y + 5y = 30 + 5y
4x = 30 + 5y
```

Divide both sides by 4:

4x / 4 = (30 + 5y) / 4
x = (30 + 5y) / 4

Therefore, the solution for x in terms of y is x = (30 + 5y) / 4.

Solving for y

Similarly, we can isolate y in the equation:

Subtract 4x from both sides:
```
4x - 5y - 4x = 30 - 4x
-5y = 30 - 4x
```

Divide both sides by -5:

-5y / -5 = (30 - 4x) / -5
y = (30 - 4x) / -5

Therefore, the solution for y in terms of x is y = (30 - 4x) / -5.

Finding Solutions

Since we have two variables and only one equation, there are infinitely many solutions for x and y that satisfy the equation. We can find specific solutions by choosing a value for either x or y and then solving for the other variable.

For example:

If x = 0:
```
y = (30 - 4(0)) / -5 
y = 30 / -5
y = -6
```
This gives us the solution (0, -6).
If y = 0:
```
x = (30 + 5(0)) / 4
x = 30 / 4
x = 7.5
```
This gives us the solution (7.5, 0).

We can continue finding more solutions by substituting different values for x or y.

Conclusion

By manipulating the equation, we have successfully expressed x and y in terms of each other. This allows us to find infinitely many solutions for x and y that satisfy the equation 4x - 5y = 30.