Question

Dimitri determined that the ordered pair (2, –2) is a solution to the system of linear equations 7x + 9y = –4 and 5x – 2y = 6 as shown.

Equation 1: 7 x + 9 y = negative 4. 7 (2) + 9 (negative 2) = negative 4. 14 + (negative 18) = negative 4. Negative 4 = negative 4. Equation 2: 5 x minus 2 y = 6. 5 (2) minus 2 (negative 2) = 6. 10 minus 4 = 6. 6 = 6.

What was Dimitri’s mistake?
He mixed up the coordinates of the ordered pair when substituting it into the equations 7x + 9y = –4 and 5x – 2y = 6.
He checked the equation 7x + 9y = –4 first when he should have checked 5 x minus 2 y = 6 first.
He made a mistake in his calculations when substituting the ordered pair into the equation 7x + 9y = –4 and simplifying.
He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.

Answer 1

To determine where Dimitri's mistake was, we need to check both equations with the ordered pair (2, -2) step by step.

**Check Equation 1: 7x + 9y = –4**

Substituting \( x = 2 \) and \( y = -2 \):

\[
7(2) + 9(-2) = 14 - 18 = -4
\]

This is correct since \( -4 = -4 \).

**Check Equation 2: 5x - 2y = 6**

Substituting \( x = 2 \) and \( y = -2 \):

\[
5(2) - 2(-2) = 10 + 4 = 14
\]

The result is \( 14 \), which does not equal \( 6 \).

Thus, Dimitri incorrectly concluded that (2, -2) is a solution to the system because, when checking the second equation, the numbers do not match.

Therefore, Dimitri’s mistake was:

**He made a mistake in his calculations when substituting the ordered pair into the equation \( 5x - 2y = 6 \) and simplifying.**