Lesson 7-2

Substitution

Definition

• The exact solution of a system of equations can be found using algebraic methods. One such method is called substitution.

Use substitution to solve the system of equations.

Ex. 1

y = 3xx + 2y = -21

Since y = 3x, substitute 3x for y in the second equation.

Solve using substitution

Use substitution to solve the system of equations.

x = 4y4x - y = 75

Solve using substitution

Ex. 2 Solve for one variable, then substitute.

x + 5y = -33x - 2y = 8

Solve for one variable, then substitute.

4x + y = 12-2x - 3y = 14

Ex. 3 Dependent System

6x - 2y = -4y = 3x = 2

Use substitution to solve the system of equations.

If a statement is true ( 4 = 4) then there are infinitely many solutions. However, if a statement is false (5 = 4) then there is no solution.

Dependent System

2x + 2y = 8x + y = -2

Use substitution to solve the system of equations.

Ex. 4 Write and Solve a System of Equaitons.

A metal alloy is 25% copper. Another metal alloy is 50% copper. How much of each alloy should be used to make 1000 grams of a metal alloy that is 45% copper.

25% Copper 50% Copper 45% Copper

Total Grams a b 1000

Grams of Copper

0.25a 0.50b 0.45(1000)

a + b = 10000.25a = 0.50b = 0.45(1000)

a + b = 10000.25a = 0.50b = 0.45(1000)

Write and Solve a System of Equations.

Gold is alloyed with different metals to make it hard enough to be used in jewelry. The amount of gold present in gold alloy is measured in 24ths called karats. 24-karat gold is 24/24 or 100% gold. Similarly, 18-karat gold is 18/24 or 75% gold. How many ounces of 18-karat gold should be added to an amount of 12-karat gold to make 4 ounces of 14-karat gold?

18-karat 12-karat 14-karat

Total Grams a b 4 ounces

Grams of Copper

0.75a 0.50b 14/24(4)

a + b = 40.75a = 0.50b = 14/24(4)

a + b = 40.75a = 0.50b = 14/24(4)