solving systems of equations by elimination name: pd algebra 3/03/09
DESCRIPTION
-3x – 5y = 23 2x + 5y = x – 5y = 23 2x + 5y = x= -4 x = 4 -3x – 5y = 23 -3(4) – 5y = – 5y = y= y = -7 Ex1: Solve the system by using elimination. { Solution (4, -7) Add systems Substitute the xTRANSCRIPT
Solving Systems of Equations by Elimination
Name: Pd
Algebra 3/03/09
Three ways to solve a system of equations:
Graphing
Elimination
Substitution
y = 2/5x – 2 y = -3x + 15{
5x + 3y = 3 2x – y = 6 {
4x – 3y = 6 y = -3x + 15{
-3x – 5y = 232x + 5y = -27
-3x – 5y = 23 2x + 5y = -27+
-1x = -4 -1 -1
x = 4-3x – 5y = 23
-3(4) – 5y = 23 -12 – 5y = 23
+12 +12-5y = 35
-5 -5y = -7
Ex1: Solve the system by using elimination.
{
Solution (4, -7)
Add systems
Substitute the x
x + 4y = -36 -5x – 4y = 52
1x + 4y = -36-5x – 4y = 52 +
-4x = 16 -4 -4
x = -41x + 4y = -36
1(-4) + 4y = -36 -4 + 4y = -36+4 +4
4y = -324 4y = -8
Ex2: Solve the system by using elimination.
{
Solution (-4, -8)
Add systems
Substitute the x
2x – 3y = -9 -2x + 3y = 10
2x – 3y = -9-2x + 3y = 10 +
0 = 1Is this true?
Ex3: Solve the system by using elimination.
{No solutions
Add systems
No!
2x + 5y = -57 -2x + 5y = -33
2x + 5y = -57-2x + 5y = -33+
10y = -90 10 10y = -9
2x + 5y = -57 2x + 5(-9) = -57
2x – 45 = -57+45 +45
2x = -122 2
x = -6
Ex4: Solve the system by using elimination.
{
Solution (-6, -9)
Add systems
Substitute the y
{ -2x – 2y = 12 3x – 2y = -33
2x 3x – 2y = -33 +
5x = -45 5 5
x = -9 3x – 2y = -33
3(-9) – 2y = -33 -27 – 2y = -33+27 +27
-2y = -6-2 -2y = 3
Ex5: Solve the system by using elimination.
Solution (-9, 3)
Add systems
Substitute the x
-1( )
+ 2y = -12
– 4y
{ -x + 4y = 2 -x + y = -1
1x-1x + 1y = -1 +
-3y = -3 -3 -3 y = 1
-1x + 1y = -1 -1x + 1(1) = -1
-1x + 1 = - 1 -1 -1
-1x = -2-1 -1
x = 2
Ex6: Solve the system by using elimination.
Solution (2, 1)
Add systems
Substitute the y
-1( )
= -2
+ 3y
{ 4x – 3y = 8 4x – 3y = 8
-4x 4x – 3y = 8 +
0 = 0Is this true?
Ex7: Solve the system by using elimination.
Infinite Solutions
Add systems
Yes! -1( )
= -8
– 4y
{ 2x + 4y = -8
x + 4y = -18
-2x 1x + 4y = -18 +
-1x = -10 -1 -1
x = 10 x + 4y = -18
10 + 4y = -18 -10 -10
4y = -28 4 4 y = -7
Ex8: Solve the system by using elimination.
Solution (10, -7)
Add systems
Substitute the x
-1( )
= 8
-3x + 3y = 6 3x + 5y = -30
-3x + 3y = 6 3x + 5y = -30+
8y = -24 8 8y = -3
3x + 5y = -30 3x + 5(-3) = -30
3x – 15 = -30+15 +15
3x = -153 3
x = -5
Ex9: Solve the system by using elimination.
{
Solution (-5, -3)
Add systems
Substitute the y
3(2y + 6) + 2y = 10
3x + 2y = 10x = 2y + 6{
6y + 18 + 2y
8y + 18 = 10 -18 -18
8y = -8 8 8
y = -1
= 10
x = 2y + 6
x = 2(-1) + 6 x = 4
Solution: (4, -1) x, y
Use substitution to solve systems.
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