Page 369 - Algebra 1

L E S S O N Solving Systems of Linear Equations
55
by Graphing
Warm Up
1. Vocabulary The
(30)
makes the equation true.
2. Evaluate 18 + 3n for n = 2.
(9)
of a linear equation is any ordered pair that
3. Is (3, 2) a solution to the equation 3x + 2y = 13? Explain. (35)
4. Write 2x + 3y = 6 in slope-intercept form. (49)
New Concepts A system of linear equations consists of two or more linear equations containing two or more variables. An example is shown below.
Math Language
A linear equation is an equation whose graph is a straight line.
3x + y = 9
x + 2y = 8
A solution of a system of linear equations is any ordered pair that makes all
the equations true.
Identifying Solutions
Tell whether the ordered pair is a solution of the given system. 3x + 2y = 7
a. (1, 2); x = 7 - 3y
SOLUTION Substitute 1 for x and 2 for y in each equation.
3x + 2y = 7 x = 7 - 3y 3(1) + 2(2) 7 1 7 - 3(2)
3+4 7 1 7-6 7=7✓1=1✓
The ordered pair (1, 2) makes both equations true. A solution of the linear system is (1, 2).
3x + 2y = 12 b. (2,3);x=7-3y
SOLUTION Substitute 2 for x and 3 for y in each equation.
Example
1
3x + 2y = 12 3(2) + 2(3) 12 6 + 6 12
12=12 ✓
x=7-3y 2 7-3(3) 2 7-9 2≠-2 ✗
Online Connection www.SaxonMathResources.com
The ordered pair (2, 3) makes only one equation true. (2, 3) is not a solution of the system.
354 Saxon Algebra 1