Simultaneous equationsIB MYP Maths Extended: Subtopic test

1. 1
   Two lines have equations $y=2x+1$ and $x+y=7$.

   (a)

   Substituting $y=2x+1$ into $x+y=7$ gives which equation?

   [1 mark]

   • A$x+2x=7$
   • B$x-2x+1=7$
   • C$3x+1=7$
   • D$3x=7+1$

   (b)

   What is the solution of this pair of equations?

   [1 mark]

   • A$x=2$, $y=5$
   • B$x=5$, $y=2$
   • C$x=3$, $y=4$
   • D$x=0$, $y=1$

   (c)

   Explain what the solution of the pair of equations tells you about the graphs of the two lines.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A pair of simultaneous equations is $3x+2y=16$ and $5x-2y=8$.

   (a)

   Which first step eliminates $y$?

   [1 mark]

   • ASubtract the second equation from the first
   • BMultiply the first equation by $2$, then add
   • CMultiply the second equation by $-1$, then add
   • DAdd the two equations

   (b)

   What is the value of $x$?

   [1 mark]

   • A$24$
   • B$3$
   • C$\frac{16}{3}$
   • D$-3$

   (c)

   Find the value of $y$, and check that your solution satisfies the other equation.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   At a bookshop in Singapore, 2 notebooks and 3 pens cost 13.50 Singapore dollars (SGD). Also, 3 notebooks and 1 pen cost 11.50 SGD.

   (a)

   Let $n$ be the price of a notebook and $p$ the price of a pen, in SGD. Write down two equations and eliminate one variable to obtain an equation in a single variable.

   [3 marks]

   (b)

   Solve your equations to find the price of a notebook and the price of a pen. Hence find the cost of 5 notebooks and 4 pens.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A school in Dubai is planning a trip for its Year 10 students and is comparing different ways to pay for transport.

   (a)

   The school hires large buses, which carry 50 students and cost 900 AED per day, and small buses, which carry 20 students and cost 400 AED per day. It uses exactly 6 buses and carries exactly 210 students with every seat filled. Let $L$ be the number of large buses and $S$ the number of small buses. Form two equations, solve them, and find the total cost for the day.

   [6 marks]

   (b)

   Two coach companies quote prices for a different trip with $n$ students. Company A charges a fixed 200 AED plus 15 AED per student. Company B charges a fixed 50 AED plus 20 AED per student.
   (i) Write an equation for the cost $C$ AED for each company.
   (ii) Find the number of students for which the two companies cost the same, and find that cost.
   (iii) For 40 students, which company is cheaper and by how much?

   [6 marks]

   Total for question 4: 12 marks

End of questions