Chapter 7 Exam Explanation

Section 1: Solving systems of equations

1.) Use graphing, substitution, or elimination to solve the system below. Explain your answer. There is more than one correct answer, as long as you explain it well enough.

3x + 2y = 4 first equation

5x -2y = 7 second equation

For the system of equations listed above, I would use the elimination method to solve for x and y. In the first equation, there is a positive 2y. In the second equation, there is a negative 2y. In knowing this information, I can eliminate the y-values to solve for x. Once I receive this answer, I substitute it into the first equation to get the value of y. My final answer is (11/8, -1/16), which is the solution to my system of equations.

Tutor note- In the future, whenever you are asked to explain your answer for selecting a method as I have shown above, please make sure that you choose a method, explain your selection step-by-step, and supply your reasoning with proof that your answer is correct.

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Shiela’s Sunglasses Shop sells sunglasses for $15.50

and visors for $12.99. On Saturday, Shiela’s Sunglasses Shop sold $396.79 worth of sunglasses and visors. If they sold 29 sunglasses and visors combined, how many sunglasses and how many visors were sold?

Tutor note- Everything in bold is the information you need to solve the problem. Everything in italics is what you need to solve for.

Use the 4 step process to solve this problem

STEP 1 Identify your variables

x = pants,   y = shirts

 

STEP 2 Write two equations

1st equation: x + y = 29     2nd equation: 15.50x + 12.99y = 396.79

 

STEP 3 Solve and check

x+y = 29 (subtract x from both sides)

y = -x + 29

Substitute y into the second equation.  15.50x + 12.99 (-x + 29) = 396.79

(multiply -x and 12.99, 12.99 and 29) 15.50x – 12.99x+376.71 = 396.79  —>

(combine like terms) 2.51x + 376.71 = 396.79 —>

(subtract 376.71 from both sides) 2.51x = 20.08 —>

(divide 2.51 on each side) 2.51x/2.51x = 20.08/2.51 —–> x = 8

Substitute x into the first equation.

8+ y = 29 —> (subtract 8 from both sides) –> y = 21

STEP 4 Write your answer as a numeric phrase

On Saturday, Shiela’s Sunglasses Shop sold 8 pairs of sunglasses and 21 visors.

GRAPHING OR SUBSTITUTION

Solve each system of equations by using the graphing or substitution method.

1. y= x + 3          x – 2y = 0

substitute your first equation for the y-value in the second equation.

x – 2(x + 3) = 0 —-> x- 2x – 6 = 0 —–> -x – 6 = 0 —–> -x -6 + 6 = 0 + 6 —-> -x/-1 = 6/-1 —-> x = -6

substitute your x-value into the first equation.

y= -6 + 3 —-> y = -3

write your solution

Solution (-6, -3)