# Video: Filling the Missing Values in a Table Using a Given Linear Relation

By using the linear relation 𝑎 + 2𝑏 = −8, fill in the missing values in the table.

02:04

### Video Transcript

By using the linear relation 𝑎 plus two 𝑏 equals negative eight, fill in the missing values in the table.

So we have 𝑎 values of two and negative eight and one 𝑏 value of negative three. So when 𝑎 equals two, we don’t know what 𝑏 is equal to. When we don’t know 𝑎’s value, we know that 𝑏 is equal to negative three. And when 𝑎 is equal to negative eight, we don’t know what 𝑏’s value is. So to find these missing values, we want to use the linear relation 𝑎 plus two 𝑏 equals negative eight.

So let’s begin by solving for 𝑏 when we know that 𝑎 is equal to two. So we will replace 𝑎 with two and then solve for 𝑏. And in order to solve for 𝑏, we need to subtract two from both sides of the equation. So we have that two 𝑏 is equal to negative 10 because negative eight minus two is negative 10. Now we must divide both sides of the equation by two. And now we’ve completely isolated 𝑏.

𝑏 is equal to negative five because negative 10 divided by two is negative five. So when 𝑎 is two, 𝑏 is equal to negative five. And we’ve plugged that in into our table. Now let’s solve for 𝑎 when 𝑏 equals negative three. So we replace 𝑏 with negative three and we solve for 𝑎. So first, two times negative three is equal to negative six. Now we need to add six to both sides of the equation. And we find that 𝑎 is equal to negative two.

So when 𝑏 was negative three, 𝑎 was equal to negative two. Now lastly, when we know that 𝑎 is equal to negative eight, we need to find what 𝑏 is equal to. So we replace 𝑎 with negative eight and solve for 𝑏. So the first thing that we need to do is to add eight to both sides of the equation. And we have that two 𝑏 is equal to zero because negative eight plus eight is zero. In isolating 𝑏, we divided by two on both sides of the equation and got that 𝑏 is equal to zero.

So when 𝑎 equals negative eight, 𝑏 equals zero. So our missing values were 𝑏 equals negative five, 𝑎 equals negative two, and 𝑏 equals zero.