4.1 Find Solutions to a Linear Equation

Find three solutions to the linear equation: $y = 9 x + 2$ .
Provide your answer as a comma-separated list of ordered pairs.
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[1] [0]

$\begin{matrix} Any set of three or more ordered pairs that are all solutions toy = 9 x + 2will be accepted. \\ Potential answers include: (0, 2), (1, 11), (–1, –7). \end{matrix}$

Step 1 of 4

We can substitute any value we want for $x$ or any value for $y$ . Since the equation is in $y$ -form, it will be easier to substitute in values of $x$ . Let’s pick $x = 0 , x = 1 , x = - 1$ .

Step 2 of 4

     $x = 0$                      $x = 1$                      $x = - 1$

     $y = 9 x + 2$          $y = 9 x + 2$          $y = 9 x + 2$

Substitute the value into the equation.
     $y = 9 \cdot 0 + 2$          $y = 9 \cdot 1 + 2$          $y = 9 \cdot - 1 + 2$

Simplify.
     $y = 0 + 2$              $y = 9 + 2$                  $y = - 9 + 2$

Simplify.
     $y = 2$                      $y = 11$                          $y = - 7$

Write the ordered pair.
     $(0, 2)$                      $(1, 11)$                      $(- 1, - 7)$

Step 3 of 4

Check.
$\begin{matrix} (0, 2) & (1, 11) & (- 1, - 7) \\ y = 9 x + 2 & y = 9 x + 2 & y = 9 x + 2 \\ 2 ≟ 9 \cdot 0 + 2 & 11 ≟ 9 \cdot 1 + 2 & - 7 ≟ 9 \cdot - 1 + 2 \\ 2 ≟ 0 + 2 & 11 ≟ 9 + 2 & - 7 ≟ - 9 + 2 \\ 2 = 2 ✓ & 11 = 11 ✓ & - 7 = - 7 ✓ \end{matrix}$

Step 4 of 4

So, $(0, 2), (1, 11), (- 1, - 7)$ are all solutions to $y = 9 x + 2$ .