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1 Simultaneous linear equations
2 are a pair of equations that work together-‐-‐that is,
3 the variables in one equation
4 are the same as the variables in another equation.
5By solving for a variable in one equation, you can solve both equations.
6 Here's how simultaneous linear equations work.
7Kate can win points by tossing rings around these bottles.
8 Different color combinations are worth different points.
9Kate wants to know how much each bottle is worth on its own.
10 If two red and two green are forty points,
11 then Kate can divide by two
12 to find that one red and one green are twenty points.
13She's closer to knowing how many points each color is worth, but isn't there yet.
14 She needs to work
15 with the other equation.
16 Subtracting one red and one green
17 leaves two red
18 worth thirty points,
19 so one red
20 must be worth
21 fifteen points.
22
23Remember how one red and one green are worth twenty points?
24 Now we
25 can see that green
26 is worth five points.
27
28 We can express the process we've just described
29 in algebraic terms
30 with two
31 simultaneous linear equations.
32 Then, we simplify where
33 we can…
34 line them up,
35
36 subtract
37 to
38 eliminate a variable…
39
40 and solve
41 for the other
42 variable.
43
44
45
46 Now we know the value of one variable,
47 we can solve
48 for the other variable.
49
50
51
52
53 By solving this pair
54 of linear
55 equations,
56 we find the
57 answer to Kate's question.
