6x-30y=120
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Y=x/5-4
The given equation is 6x - 30y = 120.
To find the values of x and y that satisfy this equation, we can rearrange it to the standard form of a linear equation, which is Ax + By = C.
First, let's simplify the equation by dividing through by the common factor of 6:
x - 5y = 20
Now, we can solve for either x or y by isolating one variable. Let's solve for x:
x = 20 + 5y
Now we have an expression for x in terms of y. We can substitute this expression into the original equation to solve for y.
6(20 + 5y) - 30y = 120
120 + 30y - 30y = 120
120 = 120
The equation is satisfied regardless of the value of y. This means that the equation represents a straight line, and any point on that line is a solution to the equation.
To find specific solutions, we can choose any value for y and substitute it into the expression for x.
For example, let's choose y = 0:
x = 20 + 5(0)
x = 20
Therefore, when y = 0, x = 20. The coordinate (20, 0) is a solution to the equation.
Similarly, we can choose another value for y, such as y = 2:
x = 20 + 5(2)
x = 30
Therefore, when y = 2, x = 30. The coordinate (30, 2) is another solution to the equation.
In summary, the equation 6x - 30y = 120 represents a line, and any point on that line is a solution to the equation.