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

2. 1 point in common NO points in common The INTERSECTION of lines
is the set of points that are common to both lines.
1 point in common
NO points in common

3. 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

4. Example #1 - using Substitution Method
(1) x - y = 0
(2) x + 3 y = 44
Substitute “y” into
other equation
Solve for “y”
Check equation (1)
4 x - y = 0
Substitute “x”
to find “y”
4x - y = 0
10 x + 3 y = 44
4 (2) - 8 ? 0
4 x = y
10 x + 3 y = 44
8 - 8 ? 0
4 (2) = y
10 x + 3 (4 x) = 44
0 = 0 √
8 = y
10 x + 12 x = 44
Check equation (2)
10 x + 3 y = 44
y = 8
22 x = 44
x = 2
10 (2) + 3 (8) ? 44
Therefore x = 2 and y = 8
written (2, 8)
? 44
44 = 44 √

5. Example #2 - using Substitution Method
Substitute “x”
Into other
equation
Solve
for “x”
(1) x + 5 y = 10
(2) x + 2 y = 12
Substitute “y”
to find “x”
Check equation (1)
2 x + 5 y = 10
x + 2 y =12
2 x + 5 y = 10
2 (40) + 5 (-14) ? 10
x = y
2 x + 5 y = 10
? 10
x = (-14)
2 (12 - 2y) + 5 y = 10
10 = 10 √
x =
y + 5 y = 10
Check equation (2)
x + 2 y = 12
x = 40
24 + y = 10
y = -14
(-14) ? 12
Therefore x = 40 and y = -14
written (40, -14)
? 12
12 = 12 √

6. Example #3 - using Addition Method
Substitute “x”
into one of the
equations
(1) x - 3 y = 27
(2) x + 3 y = 9
Eliminate “y”
by adding
(1) to (2)
Check equation (1)
2 x - 3 y = 27
2 (12) - 3 (-1) ? 27
2 x - 3 y = 27
2 x - 3 y = 27
x + 3 y = 9
2 x - 3 y = 27
? 27
2 (12) - 3 y = 27
27 = 27 √
y = 27
3 x = 36
Check equation (2)
x + 3 y = 9
- 3 y = 3
x = 12
y = -1
(-1) ? 9
Therefore x = 12 and y = -1
written (12, -1)
? 9
9 = 9 √

7. Example #4 - using Subtraction Method
(1) x + y = 18
(2) x + y = 9
Eliminate “y”
by subtracting
(2) From (1)
Substitute “x”
into one of the
equations
Check equation (1)
4 x + y = 18
4 (3) + 6 ? 18
4 x + y = 18
x + y = 9
x + y = 9
? 18
x + y = 9
18 = 18 √
3 + y = 9
3 x = 9
Check equation (2)
x + y = 9
x = 3
y = 6
3 + 6 ? 9
Therefore x = 3 and y = 6
written (3, 6)
9 = 9 √

8. Algebra Review: Systems of Equation
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!