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Solving Systems of Linear Equations of Books and Magazines

Systems of linear equations

Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price.
Harriet bought four books and three magazines for $1.45,and June bought two books and five magazines for $1.25.
What was the price of a book and what was the price of a magazine?

Solving by Substitution

Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent.

y=-3x+19
y=2x-1

y=-4x-7
y=3x

y=x+4
3y-5x=6

The Addition Method
Solve each system by addition.

x-2y=-1
-x+5y=4

3x-5y=-11
x-2y=11

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Solutions:

Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price.
Harriet bought four books and three magazines for $1.45,and June bought two books and five magazines for $1.25.
What was the price of a book and what was the price of a magazine?

Let price of each book =x
Price of each magazine=y
Harriet bought four books and three magazines for $1.45,
4x+3y=1.45 ---------------(1)

June bought two books and five magazines for $1.25.
2x+5y=1.25 ---------------(2)

Multiply equation (2) by -2, we get
-4x-10y=-2.5 ------------(3)

Adding equation (1) and equation (3), we get
4x+3y=1.45
-4x-10y=-2.5
-7y=-1.05
y=0.15

Put value of y=0.15 in equation (1), we ...

Solution Summary

There are 6 problems. Solutions to these problems explain the steps for finding the values of variables by Addition and Substitution method.

$2.19