Page 427 - Algebra 1

L E S S O N Solving Systems of Linear Equations by
63
Elimination
Warm Up
New Concepts
1. Vocabulary The graph of a equation is a straight line. (30)
Simplify.
2. 3(4x - 5)
(15)
4. ky2k3k2y5 (3)
3. 4(7y + 12) (15)
5. xy - 3xy2 + 5y2x - 4xy (18)
It is not always practical to isolate one of the variables in a system of linear equations in order to solve by substitution. Sometimes it is easier to eliminate one of the variables by combining the two equations using addition or subtraction.
Adding Equations
Solve the system by elimination and check the answer. 5x + 2y = 9
-5x + 6y = 7
SOLUTION
The two equations have equal and opposite coefficients for one of the variables, so add the equations to eliminate that variable.
y=2 Substitute 2 for
5x + 2(2) = 9 5x + 4 = 9 5x = 5 x=1
Example
1
5x + 2y = 9 -5x + 6y = 7
_____ _
8y = 16 Add equations and combine like terms.
Divide both sides by 8.
y in one of the original equations and solve for x.
Substitute 2 for y in the first equation. Multiply.
Subtract 4 from both sides.
Divide both sides by 5.
The solution is (1, 2).
Check Substitute (1, 2) for x and y in both of the original equations.
Caution
Be sure to list the values for x and y in the correct order, (x, y).
Online Connection www.SaxonMathResources.com
-5x + 6y = 7 -5(1) + 6(2) 7 -5 + 12 7
7 = 7 ✓
Substitute. Multiply. Add.
5x + 2y = 9 5(1) + 2(2) 9 5 + 4 9
9 = 9 ✓
412 Saxon Algebra 1