Question

for each ordered pair, determine whether it is a solution to $5x - 4y = 17$.

$(x,y)$	is it a solution?
$(2, 9)$	$\circ$	$\circ$
$(7, -1)$	$\circ$	$\circ$
$(-3, -8)$	$\circ$	$\circ$

Explanation:

for \((-6, 2)\):

Step1: Substitute \(x = -6\), \(y = 2\) into \(5x - 4y\)

\(5\times(-6)-4\times2\)

Step2: Calculate the value

\(5\times(-6)= -30\), \(4\times2 = 8\), so \(-30 - 8=-38\). Since \(-38
eq17\), it is not a solution.

for \((2, 9)\):

Step1: Substitute \(x = 2\), \(y = 9\) into \(5x - 4y\)

\(5\times2-4\times9\)

Step2: Calculate the value

\(5\times2 = 10\), \(4\times9 = 36\), so \(10 - 36=-26\). Since \(-26
eq17\), it is not a solution.

for \((7, -1)\):

Step1: Substitute \(x = 7\), \(y = -1\) into \(5x - 4y\)

\(5\times7-4\times(-1)\)

Step2: Calculate the value

\(5\times7 = 35\), \(4\times(-1)=-4\), so \(35-(-4)=35 + 4 = 39\). Since \(39
eq17\), it is not a solution.

for \((-3, -8)\):

Step1: Substitute \(x = -3\), \(y = -8\) into \(5x - 4y\)

\(5\times(-3)-4\times(-8)\)

Step2: Calculate the value

\(5\times(-3)=-15\), \(4\times(-8)=-32\), so \(-15-(-32)=-15 + 32 = 17\). Since \(17 = 17\), it is a solution.

Answer:

• For \((-6, 2)\): No
• For \((2, 9)\): No
• For \((7, -1)\): No
• For \((-3, -8)\): Yes