HSC Standard 2 Simultaneous Linear Equations

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A straight line has the equation of y = −x − 3. What is the y-intercept?

1 point

-1

-3

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What are the gradient and y-intercept respectively of the line y = -2x + 3?

1 point

3 and -2

-2 and 3

-2 and -3

-3 and -2

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1 point

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What is the gradient of the line shown?

1 point

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Which line below has the equation y = 4–3x?

1 point

Line a

Line b

Line c

Line d

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What is the equation of the graph shown below?

1 point

y = –2.25x

y = –9x

y = 2.25x

y = 9x

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Jim is riding his pushbike at a constant speed. He travels 60 km in 3 hours. This situation is described by the linear equation d = mt. What is the value of m?

1 point

0.05

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What is the slope of line B?

1 point

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What is the equation of line A?

1 point

y − 2x = 3

x − y = 3

y − x = 3

−2y − x = 6

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What is the simultaneous solution of the equations represented by the lines A and B?

1 point

x = −1 and y = −2

x = −1 and y = 2

x = 1 and y = −2

x = −3 and y = 3

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For the graph below, R is the revenue, in dollars, earned by a mushroom farmer selling n kilograms of mushrooms, and C is the cost, in dollars, of producing n kilograms of mushrooms. To make a profit, how many kilograms of mushrooms should the farmer’s production exceed?

1 point

100

250

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A computer application was used to draw the graphs of the equations x + y = 5 and x − y = 5. Part of the screen is shown. What is the solution when the equations are solved simultaneously?

1 point

x = 0, y = –5

x = 0, y = 5

x = 5, y = 0

x = 5, y = 5

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Jim graphed the lines y = 2x – 4 and y = 5 – x on a number plane. What is the point of intersection of the two lines?

1 point

(1, -2)

(1, 4)

(3, 1)

(3, 2)

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The graph shows the relationship between the age of a car’s engine and the car’s expected fuel consumption. Assume that the fuel price is constant over time. Which pair of graphs best represents the fuel price over time and the amount expected to be spent on fuel as this car’s engine ages?

1 point

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Last Saturday, Luke had 165 followers on social media. Rhys had 537 followers. On average, Luke gains another 3 followers per day and Rhys loses 2 followers per day.If x represents the number of days since last Saturday and y represents the number of followers, which pair of equations model this situation?

1 point

Luke: y = 165x + 3 Rhys: y = 537x – 2

Luke: y = 165 + 3x Rhys: y = 537 – 2x

Luke: y = 3x + 165 Rhys: y = 2x – 537

Luke: y = 3 + 165x Rhys: y = 2 – 537x

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For a fundraising event a school hires a cinema to show the premiere of a movie. Hiring the cinema costs $500. People are charged $10 each to attend the movie. How many people need to attend for the school to break even?

1 point

500

510

5000

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