Solving Systems of Two Linear Equations

What is the solution to this system of equations? 2x + y = 40 x - 2y = -20

• x = 10, y = 15
• x = 12, y = 16
• x = 14, y = 18
• x = 8, y = 12

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AI.9.5.C

AI.9.2.I

A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes.

Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times for a total distance of 141 miles.

This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times for a total distance of 123.75 miles.

What is the distance of the morning route in miles?

• 10.75 miles

• 8.5 miles

• 6.75 miles

• 5.25 miles

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AI.9.2.I

AI.9.5.C

What is the value of y in the solution to this system of equations? 6y + x = -59 x = -2y + 9

• -10
• 5
• 0
• -17

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AI.9.2.I

AI.9.5.C

A college student completed some courses worth 3 credits and some courses worth 4 credits. the student earned a total of 59 credits after completing 18 courses.

How many courses worth 3 credits did the students complete?

• 13 courses

• 15 courses

• 5 courses

• 3 courses

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AI.9.2.I

AI.9.5.C

What is the value of x in the solution to this system of equations? 3x - 5y = 22 y = -5x + 32

• 6.5
• -0.5

• 0.5

• -6.5

Tags

AI.9.2.I

AI.9.5.C

Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount.

The first customer paid $12 for 14 postcards and 5 large envelopes.

The second customer paid $24.80 for 10 postcards and 15 large envelopes.

What was the cost in dollars of each large envelope?

• $0.20

• $2.50

• $1.42

• $0.35

Tags

AI.9.2.I

AI.9.5.C

What is the x-value of the solution to this system of equations? x = 2y-4 7x + 5y = -66

• -2

• -6
• -8
• 10

Tags

AI.9.2.I

AI.9.5.C

A bus travels two different routes: The Green Route and the Blue Route. The routes are different lengths

On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.

On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.

What is the length of the Green Route in miles?

• 20 miles

• 5 miles

• 10 miles

• 4.5 miles

Tags

AI.9.2.I

AI.9.5.C

Mathematical Equivalence

ON

Tags

AI.9.2.I

AI.9.5.C

A manager purchased a total of 21 coffee mugs and key chains. Each coffee mug cost $8.50, each key chain cost $2.75, and the manager spent a total of $132.50. How many coffee mugs did the manager purchase?

Mathematical Equivalence

ON

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AI.9.2.I

AI.9.5.C