Christine L. answered • 12/10/14

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UCB Grad & HS Teacher: HS/College Subjects, Math, Test Prep, etc

Let x = shirts, y = slacks, z = sports coats.

Set up your systems of equations equations.

Line1: 4x + 1y = $9.45

Line2: 7x + 4y + 2z = $40.37

Line3: 5x + 1z = $15.44

Use this system of equations to eliminate y by multiplying Line1 by -4 and adding it with Line2.

Line1: -16x -4y = -37.8

Line2: 7x + 4y + 2z = 40.37

Sum: -9x + 2z = 2.57

Take the previous sum and add it to Line3 (which has been multiplied by -2)

Prev Sum: -9x +2z = 2.57

Line3: -10x - 2z= -30.88

Sum: -19x = -28.31

Solve for x.

x = -28.31/-19 = 1.49

Now plug x = 1.49 in Line1 and Simplify.

4(1.49) + 1y = $9.45

Simplify

5.96 + 1y = 9.45

Isolate y

y = 3.49

Now plug x and y values into Line2

7(1.49) + 4(3.49) + 2z = 40.37

Simplify

24.39 + 2z = 40.37

Isolate z

2z = 15.98

z = 15.98/2 = 7.99

Answer:

x = shirts = $1.49

y = pairs of slacks = $3.49

z = sports coat = $7.99

To check your work, plug back in to the original equations.

Line1: 4x + 1y = $9.45

4(1.49) + 1(3.49) = 9.45 (Perfect!)

Line2: 7x + 4y + 2z = $40.37

7(1.49) + 4(3.49) + 2(7.99) = 40.37 (Perfect!)

Line3: 5x + 1z = $15.44

5(1.49) + 1(7.99) = 15.44 (Perfect!)