Algebra Know-It-ALL
When we morphed the above two equations before mixing them on our way to a solution, we put them into SI form. Those SI equation ...
266 Two-by-Two Linear Graphs precisely draw the line through two points that are close together, we can find a third point farth ...
We Added, We Eliminated, We Can Graph In Chap. 16, we solved the following two-by-two linear system for t and u using double eli ...
268 Two-by-Two Linear Graphs When we subtract 2t from each side, we get 5 u=− 2 t− 7 We can divide through by 5 to obtain u= (−2 ...
Let’s find another point on each line to make our line-drawing task easier. If we plug in t= 3 to the SI version of the first eq ...
270 Two-by-Two Linear Graphs and u= 4 t− 3 u+ 3 = 4 t 4 t=u+ 3 t= (1/4)u+ 3/4 Now we know that the t-intercepts are −7/2 and 3/4 ...
We Renamed, We Replaced, We Can Graph In Chap. 16, we solved the following two-by-two linear system for v and w using the rename ...
272 Two-by-Two Linear Graphs upward. How about 3 units to the right? Will the w value go off the scale? Let’s plug in v= 3 and s ...
we move to the right, and ramps gradually upward as we move to the left. Let’s plug in v=− 12 and calculate: w= (−1/2)× (−12)− 5 ...
274 Two-by-Two Linear Graphs transposing the numbers in the ordered pairs. Once we’ve done these three things, we have a graph o ...
These are both functions of v. If we put these equations into SI form with v rather than w as the dependent variable, we obtain ...
276 Two-by-Two Linear Graphs When taken together as a two-by-two linear system, these equations have no common solution. That me ...
Are you confused? Suppose the graphs of a two-by-two linear system show up as parallel, vertical lines, both with undefined slop ...
278 Two-by-Two Linear Graphs (subtract 2 from s). Some of the resulting points are plotted in Fig. 17-8, along with the line con ...
Refer to Fig. 17-9. What is the equation of line L in SI form? Refer to Fig. 17-9. What is the equation of line M in SI form? U ...
280 Two-by-Two Linear Graphs becomes the independent variable and x becomes the dependent variable. We call this inverse functio ...
281 CHAPTER 18 Larger Linear Systems In this chapter we’ll solve a three-by-three linear system. That’s a triplet of linear equa ...
282 Larger Linear Systems Get the equations into form Now that we’ve chosen the variable to eliminate, we must get all three equ ...
Let’s multiply the second equation through by −3, getting − 6 x+ 15 y+ 3 z= 3 If we add this to the first equation, we obtain th ...
284 Larger Linear Systems one? Or between the first and the third, and then between the second and the third?” The answer is, “W ...
«
10
11
12
13
14
15
16
17
18
19
»
Free download pdf