Math  /  Algebra

Questiony=2x12y=2 x-12 \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 0 & \\ \hline & -2 \\ \hline 3 & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We're given an equation and a table.
We need to fill in the missing values in the table using the equation.
Basically, we plug in xx values to find yy values, and vice-versa! Watch out! Make sure you plug the values into the correct spot in the equation.
Don't mix up your xx's and yy's!

STEP 2

1. Solve for yy when x=0x = 0.
2. Solve for xx when y=2y = -2.
3. Solve for yy when x=3x = 3.

STEP 3

Alright, let's **kick things off**!
We're given the equation y=2x12y = 2x - 12 and we're told that x=0x = 0.
Our mission is to find the **mystery** yy value!

STEP 4

Let's **substitute** our **known** xx value, which is 00, into the equation: y=2012y = 2 \cdot 0 - 12

STEP 5

Now, 22 multiplied by 00 is just 00, so we have: y=012y = 0 - 12

STEP 6

And 00 minus 1212 gives us our **first answer**: y=12y = -12 Woohoo!

STEP 7

This time, we know that y=2y = -2.
Let's **plug** that into our equation: 2=2x12-2 = 2x - 12

STEP 8

To **isolate** xx, we'll **add** 1212 to **both sides** of the equation.
Remember, what we do to one side, we *must* do to the other! 2+12=2x12+12-2 + 12 = 2x - 12 + 12

STEP 9

Simplifying, we get: 10=2x10 = 2x

STEP 10

Now, we want to get xx all by itself.
Since xx is being multiplied by 22, we'll **divide both sides** by 22: 102=2x2\frac{10}{2} = \frac{2x}{2}

STEP 11

This gives us our **second answer**: 5=x5 = x or x=5x = 5.
Fantastic!

STEP 12

Almost there!
Now we're given x=3x = 3.
Let's **substitute** that into our equation: y=2312y = 2 \cdot 3 - 12

STEP 13

22 times 33 is 66, so we have: y=612y = 6 - 12

STEP 14

And 66 minus 1212 gives us our **final answer**: y=6y = -6 We did it!

STEP 15

Here's our completed table:
\begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 0 & -12 \\ \hline 5 & -2 \\ \hline 3 & -6 \\ \hline \end{tabular}

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