# Pkt Csubst

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```					Substitution Method

The purpose of the Substitution Method is to reduce two equations with two
variables down to one equation with one variable. The equation then can be solved
for the unknown.

(This method works best when one of the equations is in the form of
"x =" or "y =")

EXAMPLE: Solve for x and y:          x+y=3
y=x+5

Substitute x + 5 into          x+ y =3
the first equation in          x+(     ) =3
place of y                    x + (x +5) = 3
2x + 5 = 3
2x = -2
x = -1

Find the y value by substituting -1 into one of the original equations.

y=x+5
y = -1 + 5
Solution (-1,4)                 y=4

Check in both equations:
x+y=3             y=x+5
-1 + 4 = 3         4 = -1+ 5
3=3            4=4
EXAMPLE: Solve for x and y:         -2x + 4y = 14
y = 3x +6

Substitute 3x + 6 into        -2x + 4y = 14
the first equation in         -2x + 4( 3x + 6 ) = 14
place of y                   -2x + 12x + 24 = 14
10x + 24 = 14
10x = -10
x = -1

Find the y value by substituting -1 into one of the original equations.

y = 3x + 6
y = 3(-1) +6
Solution (-1,3)                 y = -3 +6
y=3

Check:     - 2x + 4y = 14        y = 3x + 6
-2(-1)+4(3) = 14        3 = 3(-1) +6
2 +12 = 14         3 = -3 + 6
14 =14         3=3

```
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