Question

Consider the following pair of equations:

y = –2x + 8
y = x – 1

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form. (5 points)

Answer 1

There is a special kind of substitution which some books call it by comparison.

When the two equations are both
y=some function of x
y=some other function of x, then
we can substitute the second equation into the first giving
some function of x = some other function of x and start solving.

For example,
y = –2x + 8
y = x – 1
substitute second into first
x-1=-2x+8
isolate x on left,
3x=9
x=3
second step is to substitute x=3 into second equation to get
y=x-1=3-1=2
Therefore the solution is (3,2)