Page 186 - Math Course 2 (Book 1)

Systems of Equations: Substitution

Inf nitely Many or No Solutions Let x = the number of ounces of 18-karat gold and

Use substitution to solve the system of equations. y = the number of ounces of 12-karat gold.
3x – 2y = 3 Use the table to organize the information.
–6x + 4y = –6
A. one; (0, 0) 18-karat 12-karat 14-karat
B. no solution gold gold gold
C. inf nitely many solutions Total x y 4
D. cannot be determined Ounces
Ounces 18 12 14
x
Answer of Gold 24 y (4)
24
24
The system of equations is x + y = 4 and
14
12
18
x + y = (4). Use substitution to solve this
24 24 24
system.
x + y = 4 First equation
x + y – y = 4 – y Subtract y from each side.
x = 4 – y Simplify.

12
18 x + y = (4)
14
24 24 24 Second equation
18
12
14
MO. 6 - L2b (4 – y)+ y = (4) x = 4 – y
24 24 24
Problem-Solving Using 3 1 7
Substitution 3 – y + y = Distributive Property
3
2
4
1 7
3 – y = Combine like terms
4 3
Let’s Begin 1 7
3 – y –3 = –3
4 3 Subtract 3 from each side.
1 2
– y = – Simplify.
Write and Solve a System of 4 3
Equations –4(– y) = –4(– ) Multiply each side by –4.
2
1
4 3
Example y = or 2 2 Simplify.
8
3 3

GOLD x + y = 4 First equation
2
Gold is alloyed with different metals to make it hard x + 2 = 4 y = 2 2
3 3
enough to be used in jewelry. The amount of gold
2
2
2
present in a gold alloy is measured in 24ths called x + 2 –2 = 4 –2 2 Subtract 2 from each
24 3 3 3 3
karats. 24-karat gold is or 100% gold. Similarly, side.
24
18 1
18- karat gold is or 75% gold. x = 1 Simplify.
24 3
1
How many ounces of 18-karat gold should be 1 ounces of the 18-karat gold
added to an amount of 12-karat gold to make 4 3 2
ounces of 14-karat gold? Answer and 2 ounces of the 12-karat
3
gold should be used.

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