Questions: Use substitution to determine whether the given ordered pairs are solutions of the given equation. [ (-frac56,-frac47), (0, frac67) ; 6 a+7 b=6 ] Is the ordered pair (-frac56,-frac47) a solution of the equation 6 a+7 b=6 ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. No because after substituting for a and b, it gives the result neq 6. (Type an integer or a simplified fraction.) B. Yes because after substituting for a and b, it gives the result 6=6.

Solution Steps

Substitute \( a = -\frac{5}{6} \) and \( b = -\frac{4}{7} \):

\[ 6\left(-\frac{5}{6}\right) + 7\left(-\frac{4}{7}\right) = 6 \]

Calculate \( 6\left(-\frac{5}{6}\right) \):

\[ 6 \times \left(-\frac{5}{6}\right) = -5 \]

Calculate \( 7\left(-\frac{4}{7}\right) \):

\[ 7 \times \left(-\frac{4}{7}\right) = -4 \]

Now, add the two results:

\[ -5 + (-4) = -9 \]

The left-hand side simplifies to \(-9\), while the right-hand side is \(6\). Since \(-9 \neq 6\), the ordered pair \(\left(-\frac{5}{6}, -\frac{4}{7}\right)\) is not a solution to the equation.

The correct choice is:

A. No because after substituting for \( a \) and \( b \), it gives the result \(-9 \neq 6\).

Final Answer