Download pp 7.3 example 1, 2, & 3

EXAMPLE 1
Use addition to eliminate a variable
Solve the linear system:
2x + 3y = 11
– 2x + 5y = 13
Equation 1
Equation 2
SOLUTION
STEP 1
STEP 2
STEP 3
Add the equations to
eliminate one variable.
Solve for y.
2x + 3y = 11
– 2x +5y = 13
8y = 24
y=3
Substitute 3 for y in either equation and
Solve for x.
EXAMPLE 1
Use addition to eliminate a variable
2x + 3y = 11
2x + 3(3) = 11
x=1
ANSWER
The solution is (1, 3).
Write Equation 1
Substitute 3 for y.
Solve for x.
EXAMPLE 2
Use subtraction to eliminate a variable
Solve the linear system:
4x + 3y = 2
5x + 3y = – 2
Equation 1
Equation 2
SOLUTION
STEP 1
STEP 2
Subtract the equations to
eliminate one variable.
Solve for x.
4x + 3y = 2
5x + 3y = – 2
–x
= 4
x = 4
STEP 3 Substitute 4 for x in either equation and solve
for y.
EXAMPLE 2
Use subtraction to eliminate a variable
4x + 3y = 2
Write Equation 1.
Substitute – 4 for x.
4(– 4) + 3y = 2
y=2
Solve for y.
ANSWER
The solution is (– 4, 6).
EXAMPLE 3
Arrange like terms
Solve the linear system:
8x – 4y = –4
4y = 3x + 14
Equation 1
Equation 2
SOLUTION
STEP 1
STEP 2
STEP 3
STEP 4
Rewrite Equation 2 so that the like terms are
arranged in columns.
8x – 4y = –4
8x – 4y = –4
4y = 3x + 14
3x + 4y = 14
5x
= 10
Add the equations.
Solve for x.
x=2
Substitute 2 for x in either equation and
solve for y.
EXAMPLE 3
Arrange like terms
4y = 3x + 14
4y = 3(2) + 14
y=5
Write Equation 2.
Substitute 2 for x.
Solve for y.
ANSWER
The solution is (2, 5).
GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system:
1.
4x – 3y = 5
– 2x + 3y = – 7
Equation 1
Equation 2
SOLUTION
STEP 1
STEP 2
STEP 3
4x – 3y = 5
– 2x +3y = – 7
2x = – 2
x=–1
Substitute – 1 for y in either equation and
Solve for x.
Add the equations to
eliminate one variable.
Solve for x.
GUIDED PRACTICE
for Example 1,2 and 3
4x – 3y = 5
2(– 1) – 3y = 5
y=–3
Write Equation 1.
ANSWER
The solution is (– 1, – 3).
Substitute – 1 for x.
Solve for x.
GUIDED PRACTICE
CHECK
for Example 1,2 and 3
Substitute 1 for x and 3 for y in each of the.
original equation
4x – 3y = 5
– 2x + 3y = – 7
4(– 1) – 3(– 3) =? 5
? –7
– 2(– 1) + 5(– 3) =
5 = 5
–7=–7
GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system:
2. – 5x – 6y = 8
5x + 2y = 4
Equation 1
Equation 2
SOLUTION
STEP 1
STEP 2
STEP 3
Add the equations to
eliminate one variable.
Solve for y.
– 5x – 6y = 8
5x + 2y = 4
– 4y = 12
y=–3
Substitute – 3 for y in either equation and solve
for y.
GUIDED PRACTICE
for Example 1,2 and 3
Write Equation 1.
– 5x – 6y = 8
Substitute – 3 for y.
– 5x – 6(–3) = 8
Solve for x.
x=2
ANSWER
The solution is (2, 5).
GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system:
3.
6x – 4y = 14
– 3x + 4y = 1
Equation 1
Equation 2
SOLUTION
STEP 1
STEP 2
Add the equations to
eliminate one variable.
Solve for x.
6x – 4y = 14
– 3x + 4y = 1
3x
= 15
x
= 5
STEP 3
Substitute 5 for x in either equation and solve
for y.
GUIDED PRACTICE
for Example 1,2 and 3
Write Equation 1.
6x – 4y = 14
Substitute 5 for x.
6(5) – 4y = 14
Solve for y.
y=4
ANSWER
The solution is (5, 4).
GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system:
4.
7x – 2y = 5
7x – 3y = 4
Equation 1
Equation 2
SOLUTION
STEP 1
STEP 2
Subtract the equations to
eliminate one variable.
Solve for y.
7x – 2y = 5
7x – 3y = 4
y= 1
STEP 3
Substitute 1 for y in either and solve for x.
GUIDED PRACTICE
for Example 1,2 and 3
Write Equation 1.
7x – 2y = 5
Substitute 1 for y.
7x – 2(1) = 5
Solve for x.
x=1
ANSWER
The solution is (1, 1).
GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system:
5.
3x + 4y = – 6
2y = 3x + 6
Equation 1
Equation 2
SOLUTION
STEP 1
Rewrite Equation 2 so that the like terms are
arranged in columns.
3x + 4y = – 6
3x + 4y = – 6
2y = 3x + 6
3x – 2y = – 6
STEP 2
STEP 3
STEP 4
6y = 0
Subtract the equations.
Solve for y.
y=0
Substitute 0 for y in either equation and
solve for x.
GUIDED PRACTICE
2y = 3x + 6
2(0) = 3x + 6
x=–2
for Example 1,2 and 3
Write Equation 2.
Substitute 0 for y.
Solve for x .
ANSWER
The solution is (– 2, 0).
GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system:
6.
2x + 5y = 12
5y = 4x + 6
Equation 1
Equation 2
SOLUTION
STEP 1
Rewrite Equation 2 so that the like terms are
arranged in columns.
2x + 5y = 12
2x + 5y = 12
5y = 4x + 6
– 4x + 5y = 6
STEP 2
STEP 3
STEP 4
Subtract the equations.
6x
= 6
Solve for x.
x=1
Substitute 1 for x in either equation and
solve for y.
GUIDED PRACTICE
2x + 5y = 12
2(1) + 5y = 6
x= 2
for Example 1,2 and 3
Write Equation 2.
Substitute 1 for x.
Solve for y .
ANSWER
The solution is (1, 2).