Question

Complete the table of values for the equation 9x+2y=18

Answer 1

`\large\begin{array}c\cline{2-3}&x&y\\\cline{2-3}\phantom{\frac12}&0&\boxed{9}\\\cline{2-3}\phantom{\frac12}&\boxed{2}&0\\\cline{2-3}\phantom{\frac12}&4&\boxed{-9}\\\cline{2-3}\end{array}`

Explanation:

Given equation:

`9x+2y=18`

Substitute x = 0 into the given equation and solve for y:

`\begin{aligned}x=0 \implies 9(0)+2y&=18\\2y&=18\\(2y)/(2)&=(18)/(2)\\y&=9\end{aligned}`

Substitute y = 0 into the given equation and solve for x:

`\begin{aligned}y=0 \implies 9x+2(0)&=18\\9x&=18\\(9x)/(9)&=(18)/(9)\\x&=2\end{aligned}`

Substitute x = 4 into the given equation and solve for y:

`\begin{aligned}x=4 \implies 9(4)+2y&=18\\36+2y&=18\\36+2y-36&=18-36\\2y&=-18\\(2y)/(2)&=(-18)/(2)\\y&=-9\end{aligned}`

Therefore:

`\large\begin{array}c\cline{2-3}&x&y\\\cline{2-3}\phantom{\frac12}&0&\boxed{9}\\\cline{2-3}\phantom{\frac12}&\boxed{2}&0\\\cline{2-3}\phantom{\frac12}&4&\boxed{-9}\\\cline{2-3}\end{array}`