do now pass out calculators. solve the following system by graphing: graph paper is in the back. 5x...
TRANSCRIPT
Do Now• Pass out calculators. • Solve the following system by graphing: Graph paper is in the back.
5x + 2y = 9 x + y = -3 • Solve the following system by using substitution:
11x – 7y = - 14 x – 2y = -4
Objective:
• To solve systems of equations using elimination (adding or subtracting).
Use addition to eliminate a variable
EXAMPLE 1
Solve the linear system:
2x + 3y = 11 –2x + 5y = 13
Equation 1
Equation 2
SOLUTION
Add the equations toeliminate one variable.
2x + 3y = 11–2x + 5y = 13
Solve for y. 8y = 24y = 3
STEP 1
STEP 2
Use addition to eliminate a variable
EXAMPLE 1
2x + 3y = 11 Write Equation 1
2x + 3(3) = 11 Substitute 3 for y.
x = 1 Solve for x.
ANSWER
The solution is (1, 3).
Substitute 3 for y in either equation and solve for x.
STEP 3
Use addition to eliminate a variable
EXAMPLE 1
2x + 3y = 11
11 = 11
Substitute 1 for x and 3 for y in each of the original equations.
CHECK
2(1) + 3(3) = 11?
2x + 5y = 13
13 = 13
2(1) + 5(3) = 13?
Use subtraction to eliminate a variable
EXAMPLE 2
Solve the linear system:4x + 3y = 2 Equation 1
5x + 3y = –2 Equation 2
SOLUTION
Subtract the equations toeliminate one variable.
4x + 3y = 25x + 3y = –2
Solve for x. – x = 4
STEP 1
STEP 2 x = 4
Use subtraction to eliminate a variable
EXAMPLE 2
4x + 3y = 2 Write Equation 1.
4(–4) + 3y = 2 Substitute –4 for x.
y = 6 Solve for y.
ANSWERThe solution is (–4, 6).
Substitute 4 for x in either equation and solvefor y.
STEP 3
Arrange like terms
EXAMPLE 3
Solve the linear system:8x – 4y = –4 Equation 1
4y = 3x + 14 Equation 2
SOLUTION
STEP 1 Rewrite Equation 2 so that the like terms are arranged in columns.8x – 4y = –44y = 3x + 14
8x – 4y = –43x + 4y = 14
STEP 2 Add the equations. 5x = 10
STEP 3 Solve for x. x = 2
Arrange like terms
EXAMPLE 3
4y = 3x + 14 Write Equation 2.
4y = 3(2) + 14 Substitute 2 for x.
y = 5 Solve for y.
ANSWERThe solution is (2, 5).
STEP 4 Substitute 2 for x in either equation and solve for y.
GUIDED PRACTICE for Example 1,2 and 3
Solve the linear system:
4x – 3y = 5 –2x + 3y = –7
`
1.
ANSWER (–1, –3)
GUIDED PRACTICE for Example 1,2 and 3
Solve the linear system:
5x + 2y = 45x – 6y = 8–2.
ANSWER (2, –3)
GUIDED PRACTICE for Example 1,2 and 3
Solve the linear system:6x – 4y = 143x + 4y = 1–
3.
ANSWER (5, 4)
GUIDED PRACTICE for Example 1,2 and 3
Solve the linear system:7x – 2y = 57x – 3y = 4
4.
ANSWER (1, 1)
GUIDED PRACTICE for Example 1,2 and 3
Solve the linear system:
3x + 4y = –65. = 3x + 62y
ANSWER (–2, 0)
GUIDED PRACTICE for Example 1,2 and 3
Solve the linear system:
2x + 5y = 126. = 4x + 65y
ANSWER (1, 2)