Page 397 - Algebra 1

L E S S O N Solving Systems of Linear Equations by
59
Substitution
Warm Up
1. Vocabulary A (n) to a system of linear equations is an
(55)
2. Is (-1, 3) a solution to the system below? (55)
ordered pair or set of ordered pairs that satisfies all the equations in the system.
3x + 2y = 3
x - 3y = -10
Solve each equation. 3. 3x + 7 = 5x - 28
(23)
4. 5x + 12 = 3x + 36 (26)
New Concepts To be a solution to a system of equations, an ordered pair must satisfy both equations. One method for finding solutions to systems of equations is to use
the substitution method.
Steps for Solving by Substitution
1. Rearrange one of the equations so that it is of the form y=mx+b,orx=my+b,if necessary.
2. Substitute the equivalent expression for the variable from the first step into the second equation of the system. The result is an equation with one unknown.
3. Solve the resulting equation from the second step for the variable.
4. Substitute the value of the variable from the third step into one of the
original equations to find the value of the other unknown.
5. Write the values of the unknowns as an ordered pair.
Example
1
Using Substitution
Solve the system of equations by substitution. y = 2x - 5
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y = 5x + 7
SOLUTION
y=5x+7 2x-5=5x+7 -5=3x+7
-12 = 3x -4 = x
Write the second equation. Substitute 2x - 5 for y. Subtract 2x from both sides. Subtract 7 from both sides. Divide both sides by 3.
382 Saxon Algebra 1