Section 7.3 ­ Solving Linear Systems by Linear Combination
Solving using Linear Combination
1. Arrange the equations with like terms in columns.
2. Multiply one or both of the equations by a number to obtain coefficients that are opposites for one of the variables.
3. Add the equations from Step 2. Combining like terms will eliminate one variable. Solve for the remaining variable.
4. Substitute the value obtained in Step 3 into either of the original equations and solve for the other variable.
5. Check the solution in each of the original equations.
Examples:
1. ­x + 2y = ­8
x + 6y = ­16
2. 5x ­ 4y = 3
2x + 8y = ­2
3. 3x = ­6y + 12
­x + 3y = 6
4. 10g + 3h = 10
­12g ­ 6h = ­24
5. ­3x + 5y = ­7
3x ­ 8y = 1
6. 5p = 1 + 3q
­4p + 6q = 10
7. A travel agency offers two Boston outings. Plan A includes hotel accommodations for 3 nights and two pairs of baseball tickets worth $645. Plan B includes hotel accommodations for 5 nights and four pairs of baseball tickets worth $1135.
Let x represent the cost of one night's hotel accommodation and let y represent the cost of one pair of baseball tickets. Write a system of equations you could solve to find the cost of one night's hotel accommodation and one pair of baseball tickets.
Solve the system.
Homework
WS 7.3B
#2­18 evens #19­21 all