Solving Systems Algebraically

1
Solving Systems Algebraically
Lesson 3-2
Additional Examples
Solve the system by substitution.
Step 1  Solve for one of the variables. Solving
the first equation for x is the easiest. x
3y 12 x 3y 12
Step 2  Substitute the expression for x into the
other equation. Solve for y.
2x 4y 9 2(3y 12) 4y
9 Substitute for x. 6y 24 4y
9 Distributive Property 6y 4y
33 y 3.3
Step 3  Substitute the value of y into either
equation. Solve for x. x 3(3.3) 12 x
2.1
The solution is (2.1, 3.3).
2
Solving Systems Algebraically
Lesson 3-2
Additional Examples
At Renaldis Pizza, a soda and two slices of the
pizzaoftheday costs 10.25. A soda and four
slices of the pizzaoftheday costs 18.75. Find
the cost of each item.
2p s 10.25 Solve for one of the
variables. s 10.25 2p  
3
Solving Systems Algebraically
Lesson 3-2
Additional Examples
(continued)
4p (10.25 2p) 18.75 Substitute the
expression for s into the other equation.
Solve for p. p 4.25
2(4.25) s 10.25 Substitute the value of p
into one of the equations. Solve for s.
s 1.75
The price of a slice of pizza is 4.25, and the
price of a soda is 1.75.
4
Solving Systems Algebraically
Lesson 3-2
Additional Examples
Use the elimination method to solve the system.
y 3
3x y 9 Choose one of the original
equations.
3x (3) 9 Substitute y. Solve for x.
x 2
The solution is (2, 3).
5
Solving Systems Algebraically
Lesson 3-2
Additional Examples
Solve the system by elimination.
To eliminate the n terms, make them additive
inverses by multiplying.
m 4 Solve for m.
2m 4n 4 Choose one of the original
equations. 2(4) 4n 4 Substitute for
m. 8 4n 4
4n 12 Solve for n. n 3
The solution is (4, 3).
6
Solving Systems Algebraically
Lesson 3-2
Additional Examples
Solve each system by elimination.
a. 3x 5y 6 6x 10y 0
Elimination gives an equation that is always
false.
The two equations in the system represent
parallel lines.
The system has no solution.
7
Solving Systems Algebraically
Lesson 3-2
Additional Examples
(continued)
b. 3x 5y 6 6x 10y 12
Elimination gives an equation that is always true.
The two equations in the system represent the
same line.
The system has an infinite number of solutions