Question

for each ordered pair, determine whether it is a solution to (3x + 5y=- 17).
\begin{tabular}{|c|c|c|}hline((x,y))&multicolumn{2}{|c|}{is it a solution?}\cline{2 - 3}&yes&no\hline((-8,3))&(\bigcirc)&(\bigcirc)\hline((7,2))&(\bigcirc)&(\bigcirc)\hline((6, - 7))&(\bigcirc)&(\bigcirc)\hline((-4,-1))&(\bigcirc)&(\bigcirc)\hlineend{tabular}

Explanation:

Step1: Check (-8, 3)

Substitute \( x = -8 \), \( y = 3 \) into \( 3x + 5y \):
\( 3(-8) + 5(3) = -24 + 15 = -9
eq -17 \). So No.

Step2: Check (7, 2)

Substitute \( x = 7 \), \( y = 2 \) into \( 3x + 5y \):
\( 3(7) + 5(2) = 21 + 10 = 31
eq -17 \). So No.

Step3: Check (6, -7)

Substitute \( x = 6 \), \( y = -7 \) into \( 3x + 5y \):
\( 3(6) + 5(-7) = 18 - 35 = -17 \). So Yes.

Step4: Check (-4, -1)

Substitute \( x = -4 \), \( y = -1 \) into \( 3x + 5y \):
\( 3(-4) + 5(-1) = -12 - 5 = -17 \). So Yes.

Answer:

(x, y)	Yes	No
(7, 2)		✔️
(6, -7)	✔️
(-4, -1)	✔️