1. Vocabulary: Chapter Section 5.2.3 Topic: Simultaneous Linear Equations
An equation has an equal sign.
A linear equation can be drawn on an xy graph. It is a straight line.
Simultaneous Linear Equations can be solved to find the point where two lines cross on an xy graph.

2. Example One.
Instructions: Solve the system of equations by using substitution.
-10
-10 ÷5 ÷5

3. Example Two.
Instructions: Solve the system of equations by using substitution.
+15
+15
÷10
÷10

4. Example Three.
Instructions: Solve the system of equations by using substitution. -6 -6 -x -x

5. Classwork One
Instructions: Solve the system of equations by using substitution.

6. 2x 2x = 8 x = 4 3x + 4y = 20 x + 4y = 12 x + 4y = 12 3x + 4y = 20
Example One
Instructions:
Use elimination. Find the (x,y) coordinates where the lines cross.
3x + 4y = 20 x + 4y = 12
x + 4y = 12
3x + 4y = 20
(4) + 4y = 12
-( x + 4y = 12 ) 2x 8 -4 -4
2x = 8
4y = 8 ÷2 ÷2 ÷4 ÷4
x = 4
(4,2)
y = 2

7. x x = 4 2x + 3y = 5 x + 3y = 1 x + 3y = 1 2x + 3y = 5 (4) + 3y = 1
Example Two
Instructions:
Use elimination. Find the (x,y) coordinates where the lines cross.
2x + 3y = 5 x + 3y = 1
x + 3y = 1
2x + 3y = 5
(4) + 3y = 1
-( x + 3y = 1 ) x 4 -4 -4
x = 4
3y = -3 ÷3 ÷3
(4,-1)
y = -1

8. 8x 8x = 16 x = 2 5x - 6y = -32 3x + 6y = 48 3x + 6y = 48 5x - 6y = -32
Example Three
Instructions:
Use elimination. Find the (x,y) coordinates where the lines cross.
5x - 6y = x + 6y = 48
3x + 6y = 48
5x - 6y = -32
+( 3x + 6y = 48 )
3(2) + 6y = 48
6+ 6y = 48 8x 16
8x = 16 -6 -6
6y = 42
x = 2
(2,7)
÷ ÷6
y = 7

9. Classwork One
Instructions: Solve the system of equations by using elimination.

10. Classwork One
Instructions: Solve the system of equations by using substitution.

11. 3( ) 5y 5y = 10 y = 2 x + 3y = 5 3x + 4y = 5 3x + 9y = 15 3x + 4y = 5
Example One. Instructions: Use elimination. Find the (x,y) coordinates where the lines cross.
x + 3y = 5 3x + 4y = 5 3( )
3x + 9y = x + 4y = 5
3x + 4y = 5
3x + 9y = 15
-( 3x + 4y = 5 )
3x + 4(2) = 5
3x + 8 = 5 5y 10
5y = 10 -8 -8
3x = -3
y = 2
(2, -1)
x = -1

12. 2( ) 3( ) -5x -5x = -5 x = 1 2x + 3y = 5 3x + 2y = 5
Example Two Instructions: Use elimination. Find the (x,y) coordinates where the lines cross.
2x + 3y = 5 3x + 2y = 5 2( ) 3( )
4x + 6y = x + 6y = 15
9x + 6y = 15
4x + 6y = 10
-( 9x + 6y = 15 )
9(1) + 6y = 15
9 + 6y = 15
-5x -5
-5x = -5 -9 -9
6y = 6
x = 1
(1,1)
y = 1