Expert: Josh - 3/29/2005

Question
solve each system of equation using either elimination, or substiution.

4a - b = 26
8a -b = 54

3s -2t = 10
4s +t = 6

Answer
Christy, it's important that you understand the ideas behind this. Given two equations and two unknowns, "a" and "b", we can determine the values of "a" and "b" by eliminating one piece of information at a time.

4a - b = 26  ...[#1]
8a -b = 54 ..[#2]

From [#1], make "b" the subject, by adding "b-26" to both sides of the equation. We get b=4a-26. Putting this into [#2],
8a-b=54
8a-(4a-26)=54
4a+26=54
4a=54-26
4a=28
a=28/4=7

putting this back into [#1], we get,

4*7-b=26
28-b=26
b=2

Now try doing the second question using the method of elimination.

3s -2t = 10 ..[#3]
4s +t = 6  ..[#4]
Let us eliminate the variable "t" first.
Multiply [#4] by 2.
This gives
8s+2t=12 ...call this [#5]
Adding [#3] and [#5], we get
3s-2t+(8s+2t)=10+12
11s=22
Therefore, s=2. From [#4],4*2+t=6, so, t=-2.