Download Chapter 1 Points, Lines, Planes, and Angles page 1

Algebra Review
Systems of Equations
page 69
Ways to Solve a System of Equations:
1) Graph Method - will be taught in algebra 2
2) Substitution Method
3) Addition / Subtraction Method
The INTERSECTION of lines
is the set of points that are common to both lines.
1 point in common
NO points in common
When the intersection of lines is one point …
it is identified by an “x” value and a “y”
value …
and is written as an ordered pair,
(x,y).
y axis
(x,y)
x axis
Example #1 - using Substitution Method
(1)
Solve for “y”
Substitute “x”
- y =“y”
0
to4xfind
(2)
4x- y = 0
Substitute “y” into
10 x +other
3 y = 44equation
10 x + 3 y = 44
4x=y
10 x + 3 y = 44
4 (2) = y
10 x + 3 (4 x) = 44
8=y
10 x + 12 x = 44
y=8
22 x = 44
x=2
Therefore x = 2 and y
=8
written (2, 8)
Check equation (1)
4x-y=0
4 (2) - 8 ? 0
8-8?0
0=0
Check equation (2)
10 x + 3 y = 44
10 (2) + 3 (8) ? 44
20 + 24 ? 44
44 = 44
Example #2 - using Substitution Method
Substitute “x”
Solve
(1)
2Into
x + 5 other
y = 10
for “x”
equation
(2)
x + 2 y = 12
Check equation (1)
Substitute “y”
2 x + 5 y = 10
x + 2 y =12 to find “x”
2 x + 5 y = 10
x = 12 - 2y
x = 12 - 2 (-14)
x = 12 + 28
x = 40
2 x + 5 y = 10
2 (12 - 2y) + 5 y = 10
24 - 4 y + 5 y = 10
24 + y = 10
y = -14
Therefore x = 40 and y = -14
written (40, -14)
2 (40) + 5 (-14) ? 10
80 - 70 ? 10
10 = 10
Check equation (2)
x + 2 y = 12
40 + 2 (-14) ? 12
40 - 28 ? 12
12 = 12
Example #3 - using Addition Method
(1)
Eliminate “y”
by adding
(1) to (2)
(2)
Substitute
2 x - 3 y = 27 “x”
into one of the
x+3y= 9
equations
Check equation (1)
2 x - 3 y = 27
2 x - 3 y = 27
2 (12) - 3 (-1) ? 27
(1)
2 x - 3 y = 27
2 x - 3 y = 27
24 + 3 ? 27
(2)
x+3y= 9
2 (12) - 3 y = 27
27 = 27
3x
= 36
24 - 3 y = 27
Check equation (2)
x = 12
-3y=3
y = -1
x+3y= 9
Therefore x = 12 and y = -1
written (12, -1)
12 + 3 (-1) ? 9
12 - 3 ? 9
9= 9
Example #4 - using Subtraction Method
(1)
Eliminate “y”
by subtracting
(2) From (1)
(2)
4 x + y = 18
Substitute “x”
x+ y= 9
into one of the
equations
Check equation (1)
4 x + y = 18
4 (3) + 6 ? 18
(1)
(2)
4 x + y = 18
x+y=9
x+y= 9
x+y=9
3x
= 9
3+y=9
x= 3
y=6
Therefore x = 3 and y = 6
written (3, 6)
12 + 6 ? 18
18 = 18
Check equation (2)
x+y= 9
3+6? 9
9= 9
Assignment
Algebra Review: Systems of Equation
on pages 69
1 to 17 odd numbers
You must know how to solve a system of
equations with two (2) variables and
two (2) equations for
Honors Geometry!