Questions: Determine whether the ordered pair is a solution for the equation. (1,5) ; (7/3) x-y=5

Transcript text: Determine whether the ordered pair is a solution for the equation. $(1,5) ; \frac{7}{3} x-y=5$

Solution

Solution Steps

To determine if the ordered pair $(1, 5)$ is a solution to the equation $\frac{7}{3}x - y = 5$, substitute $x = 1$ and $y = 5$ into the equation. If both sides of the equation are equal after substitution, then the ordered pair is a solution.

Step 1: Substitute the Ordered Pair into the Equation

To determine if the ordered pair $(1, 5)$ is a solution to the equation $\frac{7}{3}x - y = 5$, substitute $x = 1$ and $y = 5$ into the equation:

\[ \frac{7}{3} \times 1 - 5 \]

Step 2: Simplify the Expression

Calculate the left side of the equation:

\[ \frac{7}{3} \times 1 = \frac{7}{3} \]

Subtract $5$ from $\frac{7}{3}$:

\[ \frac{7}{3} - 5 = \frac{7}{3} - \frac{15}{3} = -\frac{8}{3} \]

Step 3: Compare Both Sides of the Equation

The left side of the equation is $-\frac{8}{3}$ and the right side is $5$. Since $-\frac{8}{3} \neq 5$, the ordered pair $(1, 5)$ is not a solution to the equation.