Question

LOGICAL REASONING In Exercises \(56-59\), tell whether the statement is true or false. Justify your answer. The point \((3,5)\) is on the graph of \(3 x+5 y=30\)

Short answer

The statement is false. The point \((3,5)\) is not on the graph of \(3 x + 5 y = 30\) since on substituting the point into the equality, both sides of the equation are not equal.

Step-by-step solution

Substitute the point into the equation

Replace \(x\) in the equation with 3 and \(y\) with 5.\n It becomes: \(3*3 + 5*5\).

Compute the equation

Calculate the left side of the equation. \(3*3 + 5*5 = 9 + 25 = 34\).\n Now, compare this with the right side of the equation, which is 30.

Comparing both sides

As 34 is not equal to 30. The left hand side is not equal to the right hand side of the equation after substituting the given point into it. Therefore, the point \((3,5)\) does not lie on the graph of the given equation.