Question

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 \(3x + 2y\): \(3(9)+2(0)=27+0 = 27
eq18\). Not a solution.

Step4: Check (0,6)

Substitute \(x = 0\), \(y = 6\) into \(3x + 2y\): \(3(0)+2(6)=0 + 12 = 12
eq18\). 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)