Simultaneous Linear Equations

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Simultaneous Linear Equations — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionSolving by Elimination MethodConcept Practice

4 marks~6 minCriterion A

A city planner models two pedestrian pathways on a coordinate grid. Pathway P follows the line

2x + y = 8

and Pathway Q follows the line

x - y = 1

. The pathways intersect at a single point, which marks the location of a proposed information kiosk.

Use the elimination method to find the exact coordinates of the intersection point. [2]

The kiosk must be placed at least 2.5 units from the origin to avoid underground utilities. Justify whether the proposed location satisfies this requirement. [2]

Solutions

2QuestionSolving by Elimination MethodAssessment Practice

4 marks~6 minCriterion D

A small business owner models monthly revenue and cost (in dollars) as:

R = 15x \qquad C = 2000 + 8x

where

x

is the number of units sold, the selling price is 15 dollars per unit, the fixed monthly rent is 2000 dollars, and the variable material cost is 8 dollars per unit.

Use the elimination method to find the break-even value of

x

, where

R = C

. State your answer as a whole number of units and justify your rounding. [2]

The business introduces a bulk discount for large orders and experiences seasonal demand fluctuations. Advise the business owner whether this linear model should be used to predict profit under these conditions, citing the specific assumptions that are affected. [2]

Solutions

3QuestionSolving GraphicallyAssessment Practice

4 marks~6 minCriterion C

A city planner models two road-cost proposals using the equations

y = 2x - 1

and

y = -x + 5

, where

x

is years after the project starts and

y

is cost in millions of dollars. The graph of both lines is shown.

State the coordinates of the intersection point of the two lines. [1]

Interpret what the intersection point represents in terms of the two cost models. [1]

The planner states: "The two proposals reach equal cost at exactly year 2." Justify whether this claim is correct, showing your algebraic reasoning. [2]

Solutions

4QuestionSolving by Substitution MethodAssessment Practice

4 marks~6 minCriterion B

A logistics company tracks two delivery routes. Each day, the total distance covered by both routes is

a

km, and the difference between the longer and shorter route is

b

km. The distances

x

(longer) and

y

(shorter), in km, satisfy:

x + y = a \qquad x - y = b

Deduce the values of

x

and

y

for each system. [1]

System 1:

a = 5,\ b = 1

\quad

System 2:

a = 7,\ b = 3

System 3:

a = 10,\ b = 4

\quad

System 4:

a = 12,\ b = 2

Deduce general formulas for

x

and

y

in terms of

a

and

b

. [1]

Prove that your formulas satisfy both original equations. [1]

The company requires the shorter route to be at least 30% of the total daily distance. For

a = 40

and

b = 10

, advise the company whether this scheduling requirement is met, justifying your answer using your formulas. [1]

Solutions

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