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

Fill in the Blanks

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.