Problem 133 - Introductory Algebra for College Students

Question

Is \(x-4 y=14\) a true statement for \(x=12\) and \(y=1 ?\)

Step-by-Step Solution

Answer

No, the given equation \(x-4y=14\) is not true for \(x=12\) and \(y=1\).

Step 1: Substitution of the Values

Substitute the given values of \(x\) and \(y\) into the equation. The equation is \(x-4y=14\) and the given values are \(x=12\) and \(y=1\). Let's replace \(x\) and \(y\) with these values. So, we have \(12 - 4*1 = 14\).

Step 2: Simplify the Left-Hand-Side

Simplify the left side of the equation that we get in step 1. From the calculation \(12 - 4*1\), we get 8.

Step 3: Check the Equality

Now check if the left-hand-side is equal to the right-hand-side of the equation. We have 8 equals to 14, but according to the laws of mathematics, 8 is not equal to 14. Therefore, the equation is not true for the given values of \(x\) and \(y\).