Simultaneous Linear Equations

You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 91 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Simultaneous Linear Equations — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionChecking Solutions for Both EquationsConcept Practice

2 marks~3 minCriterion A

A city planner models two proposed road alignments on a coordinate grid. Road 1 follows

y = 2x + 1

and Road 2 follows

y = -x + 4

. A junction is planned at point

P(1, 3)

.

Justify that

P(1, 3)

is the junction point of the two roads by verifying it satisfies both equations. [2]

Solutions

2QuestionChecking Solutions for Both EquationsAssessment Practice

4 marks~6 minCriterion D

A city planner models two road-widening proposals. Proposal A follows the cost equation

y = x - 1

and Proposal B follows

y = -x + 5

, where

x

is the number of months into the project and

y

is the projected budget surplus (in millions of dollars). The graph shows both lines intersecting at point

P

State the coordinates of

P

from the graph. [1]

Show that

P

satisfies both equations simultaneously. [2]

Interpret what the coordinates of

P

mean in this context, and advise the city planner whether

P

should be used as the basis for deciding when both proposals are financially equivalent. [1]

Solutions

3QuestionSolving GraphicallyAssessment Practice

4 marks~6 minCriterion C

A city planner models two proposed road alignments as straight lines on a coordinate grid. The graph shows both lines.

Line 1 passes through

(0, 1)

and

(2, 5)

.
Line 2 passes through

(0, -3)

and

(2, 1)

Deduce the gradient of each line from the graph. [1]

Explain why the two roads will never intersect, using the properties of both lines. [2]

Advise the city planner whether a single crossing point between the two roads can ever be achieved by extending them indefinitely, and justify your advice. [1]

Solutions

4QuestionChecking Solutions for Both EquationsAssessment Practice

6 marks~9 minCriterion B

A logistics company tracks two delivery variables,

x

(vehicles dispatched) and

y

(spare vehicles held in reserve), which satisfy:

2x + y = 10

x - y = c

where

c

is a whole-number demand index set each morning.

Solve the system for

c = 2

c = 5

, and

c = 8

. Present your solutions as:

$c$	2	5	8
$(x, y)$	___	___	___ [2]

Analyse how

x

and

y

each change as

c

increases by 3. Hence deduce a general rule expressing

x

and

y

in terms of

c

. [2]

The company requires at least one spare vehicle (

y \geq 1

) to operate safely. Using your general rule, determine the maximum whole-number value of

c

for which this condition is met, and advise the operations manager whether the company can operate safely when

c = 14

. [2]

Solutions

Questions 5-95

Unlock these questions with Premium

That's every free question here — 4 of 95.

+91 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade