Word Problem: Systems of Linear Equations

WORD PROBLEMS INVOLVING SYSTEMS OF LINEAR EQUATIONS

Multiple Choice

REVIEW TIME:

Which equation is the slope-intercept form?

• y = mx + b

• y = bx + m

• x = my + b

• y = x + b

Multiple Choice

REVIEW TIME:

In the slope-intercept form: y = mx + b, what letter represents the slope?

• slope = y

• slope = m

• slope = b

• slope = x

Multiple Choice

REVIEW TIME:

Which one is the same thing as the meaning of slope?

• vertical intercept

• rate of change

• coefficient

• constant

Multiple Choice

REVIEW TIME:

In the slope-intercept form: y = mx + b, how about the y-intercept?

• y-intercept = y

• y-intercept = x

• y-intercept = b

• y-intercept = m

Multiple Select

REVIEW TIME:

Which one is the same meaning as the y-intercept?

• starting value

• rate

• initial value

• change

Multiple Choice

SITUATION:

John would like to save money to buy a new phone. He started saving with $75 and keep adding $5 per week. Which value represents the slope?

• $75

• $5

Multiple Choice

SITUATION:

John would like to save money to buy a new phone. He started saving with $75 and keep adding $5 per week. Which value represents the y-intercept?

• $75

• $5

Multiple Choice

SITUATION:

John would like to save money to buy a new phone. He started saving with $75 and keep adding $5 per week. If y represents the total savings, and x represents the number of weeks, what equation will represent the given situation?

• y = 5x + 75

• y = 75x + 5

• y = 5x

• y = 75x

Example 1:

​John and Mary would like to save money for summer camp. John started saving with $10 and adding $3 per week. Mary, on the other hand started with $15 and adding $2 per week.

Example 1:

​John and Mary would like to save money for summer camp. John started saving with $10 and adding $3 per week. Mary, on the other hand started with $15 and adding $2 per week.

​Representation:

Multiple Choice

John started saving with $10 and adding $3 per week.

What equation best describes the savings of John?

• y = 10x +3

• y = 3x - 10

• y = 3x + 10

• y = 10x - 3

Multiple Choice

Mary started saving with $15 and adding $2 per week.

What equation best describes the savings of Mary?

• y = 2x + 15

• y = 2x - 15

• y = 15x + 2

• y = 15x - 2

Multiple Choice

John and Mary would like to save money for summer camp. John started saving with $10 and adding $3 per week. Mary, on the other hand started with $15 and adding $2 per week.

Which systems of linear equation best describes John's and Mary's savings?

• y = 2x + 15

  y = 3x + 10

• y = 2x - 15

  y = 3x - 10

• y = 15x + 2

  y = 10x + 3

• y = 15x - 2

  y = 10x - 3

Multiple Choice

John: y = 3x + 10

Mary: y = 2x + 15

What equation will you get after applying substitution?

• y = 3(2x + 15) + 10

• y = 2(3x + 10) + 15

• 3x + 10 = 2x + 15

• 3x + 15 = 2x + 10

Multiple Choice

John: y = 3x + 10

Mary: y = 2x + 15

In how many weeks will John and Mary's savings be equal?

• 5 weeks

• 6 weeks

• 7 weeks

• 4 weeks

Multiple Choice

John: y = 3x + 10

Mary: y = 2x + 15

How much will their savings be in 5 weeks?

• $25

• $20

• $35

• $30

Example 2:

​Two spiders are climbing up a wall. The first one is at a height of 8 feet from the ground and climbs at a speed of 6 feet per minute. The second is at a height of 20 feet from the ground and climbs 3 feet per minute.

​Representation:

Multiple Choice

Two spiders are climbing up a wall. The first one is at a height of 8 feet from the ground and climbs at a speed of 6 feet per minute. The second is at a height of 20 feet from the ground and climbs 3 feet per minute.

What equation will best represent the total height of each spider?

• y = 6x + 8

  y = 20x + 3

• y = 6x + 8

  y = 3x + 20

• y = 8x + 6

  y = 3x + 20

• y = 6x - 8

  y = 3x - 20

Multiple Choice

After substituting Equation 1 to Equation 2, what equation will you get?

• 6x + 20 = 3x + 8

• y = 3(6x + 8) + 20

• 6x + 8 = 3x + 20

• y = 6(3x + 20) + 8

Multiple Choice

Two spiders are climbing up a wall. The first one is at a height of 8 feet from the ground and climbs at a speed of 6 feet per minute. The second is at a height of 20 feet from the ground and climbs 3 feet per minute.

In how many minutes will the spiders have the same height on the wall?

• 3 minutes

• 4 minutes

• 1 minute

• 2 minutes

Multiple Choice

Two spiders are climbing up a wall. The first one is at a height of 8 feet from the ground and climbs at a speed of 6 feet per minute. The second is at a height of 20 feet from the ground and climbs 3 feet per minute.

In how many feet will the two spiders have the same height?

• 30 feet

• 31 feet

• 28 feet

• 32 feet

LET'S TRY THIS!

​REPRESENTATION:

Multiple Choice

What equation can be represented on the first bulleted statement?

• y = 6x + 3

• 6x + 3y = 27.75

• 3x + 6y = 27.75

• x + y = 27.75

Multiple Choice

What equation can be represented on the second bulleted statement?

• y = x + 1.75

• y = 1.75x

• y = x - 1.75

• x + y = 1.75

Multiple Choice

Using the Desmos graphing calculator, what is the solution (x, y) of the systems of linear equation based on the situation?

• (2.5, 4.25)

• (4.25, 2.5)

• (2.5)

• (4.25)

Fill in the Blanks

How much is the cost for each hotdog? Fill in numerical value only.

Fill in the Blanks

How much is the cost for each hamburger? Fill in numerical value only.

Multiple Select

SELF-ASSESSMENT:

Rate 1-5, 1 being the lowest and 5 being the highest. How much did you understand the lesson today?

• 1

  It's so complicated and difficult. Needs one-on-one help.

• 2

  I need more practice and reteaching.

• 3

  I understand it but needs more practice and monitoring.

• 4

  I understand it and I need more time to work with a problem.

• 5

  I highly understand and I can do more problems independently.