Question

problem 1
this graph shows the line $3x + 2y = 18$.
select all of the points that are solutions to the equation.
$\square$ $(2, 6)$
$\square$ $(6, 0)$
$\square$ $(9, 0)$
$\square$ $(0, 6)$
$\square$ $(0, 9)$

Explanation:

Step1: Check (2,6)

Substitute \(x = 2\), \(y = 6\) into \(3x + 2y\):
\(3(2)+2(6)=6 + 12=18\). So (2,6) is a solution.

Step2: Check (6,0)

Substitute \(x = 6\), \(y = 0\) into \(3x + 2y\):
\(3(6)+2(0)=18+0 = 18\). So (6,0) is a solution.

Step3: Check (9,0)

Substitute \(x = 9\), \(y = 0\) into \(3x + 2y\):
\(3(9)+2(0)=27+0 = 27
eq18\). So (9,0) is not a solution.

Step4: Check (0,6)

Substitute \(x = 0\), \(y = 6\) into \(3x + 2y\):
\(3(0)+2(6)=0 + 12=12
eq18\). So (0,6) is not a solution.

Step5: Check (0,9)

Substitute \(x = 0\), \(y = 9\) into \(3x + 2y\):
\(3(0)+2(9)=0 + 18=18\). So (0,9) is a solution.

Answer:

(2, 6), (6, 0), (0, 9)