Algebra Know-It-ALL

Suppose we move from (0, b) to some point (x,y) on the line by going Δx units to the right and Δy units upward. The x coordinate ...

246 Graphs of Linear Relations But in this situation, Δx is exactly equal to x! That’s because, by traversing the increment Δx, ...

As before, we have mΔx=Δy Observe that in Fig. 15-7, y=y 0 +Δy Let’s substitute mΔx for Δy here. That gives us y=y 0 +mΔx Now we ...

248 Graphs of Linear Relations which is the same as y= 3 x − 2 When we work with the PS form, we come across another “sign-rigid ...

Now let’s use the PS form to derive an equation for the line. We have two points to choose from. Either point will work. Let’s u ...

250 Graphs of Linear Relations Imagine two points P and Q plotted on the Cartesian plane, where the independent variable is u a ...

251 CHAPTER 16 Two-by-Two Linear Systems In Chap. 12, we saw how we can solve first-degree equations in one variable. Now it’s t ...

252 Two-by-Two Linear Systems Dividing through by 4, we get y=− 2 x+ 4 Now for the second equation. We begin with 7 x−y= 41 Subt ...

Two versions of the SI form In a two-by-two system, it often doesn’t matter which variable we consider independent and which one ...

Solution Letx represent the airspeed of the plane, and let y represent the speed of the wind, both in kilometers per hour. When ...

These values should be checked by plugging them into both of the original equations to be sure they’re correct. Here we go: x+y= ...

256 Two-by-Two Linear Systems Adding the two morphed equations in their entirety causes the variable t to vanish: − 4 t+u=− 3 4 ...

That works! The second original equation comes out like this: u= 4 t− 3 −17/11= 4 × 4/11 − 3 −17/11= 16/11 − 3 −17/11= 16/11 − 3 ...

258 Two-by-Two Linear Systems The terms eby and −bey are additive inverses, so they disappear from the sum. Next, we can apply t ...

Then we can subtract 10 from each side to obtain this SI equation with w playing the role of the dependent variable: w= 7 v− 10 ...

260 Two-by-Two Linear Systems Are you confused? As always, we had better check our work to be sure the solutions we obtained sat ...

Now we can substitute (4x+ 2) for y in the first original equation, obtaining 3 x−π(4x+ 2) =− 1 When we apply the distributive l ...

262 Two-by-Two Linear Systems Applying the distributive law, we get y= (− 4 + 8 π+ 6 − 8 π)/(3− 4 π) When we add up the terms in ...

When we attempt to solve the following two-by-two linear system, we will fail. Try it using the double-elimination method and s ...

264 CHAPTER 17 Two-by-Two Linear Graphs Let’s graph the two-by-two linear systems we looked at in Chap. 16. This will give you a ...