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Linear Graphs and Simultaneous Linear Equations

Secondary 2 practice

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Linear Graphs and Simultaneous Linear Equations practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise Linear Graphs and Simultaneous Linear Equations free

What this topic covers

Worked examples

Example 1

Using the elimination method, solve the simultaneous equations 2x+4y=−42x + 4y = -4 and 4x+5y=−114x + 5y = -11. Find the values of x and y.
Show the worked solution
  • Label the equations:
  • 2x+4y=−4⋯(1)2x + 4y = -4 \quad \cdots (1)
  • 4x+5y=−11⋯(2)4x + 5y = -11 \quad \cdots (2)
  • (1)×2(1) \times 2: make xx-coefficients equal
  • 4x+8y=−8⋯(3)4x + 8y = -8 \quad \cdots (3)
  • (3)−(2)(3) - (2): eliminate xsubtractx \quad \scriptsize\textit{subtract}
  • 3y=33y = 3
  • y=1y = 1

Answer: x=−4,y=1x=-4,y=1

Example 2

Using the substitution method, solve the simultaneous equations x+y=4x + y = 4 and 2x−y=112x - y = 11. Find the values of x and y.
Show the worked solution
  • Label the equations:
  • x+y=4⋯(1)x + y = 4 \quad \cdots (1)
  • 2x−y=11⋯(2)2x - y = 11 \quad \cdots (2)
  • From (1)(1), rearrange to make yy the subject: rearrange\quad \scriptsize\textit{rearrange}
  • y=4−x⋯(3)y = 4 - x \quad \cdots (3)
  • Substitute (3)(3) into (2)(2): substitute\quad \scriptsize\textit{substitute}
  • 2x−(4−x)=112x - \left(4 - x\right) = 11
  • 2x−4+x=112x - 4 + x = 11

Answer: x=5,y=−1x=5,y=-1

Example 3

Admission tickets to the zoo have one price for an adult and another for a child. A group of 77 adults and 44 children paid $73\$73 in total. Another group paid $96\$96 for 66 adults and 99 children. Find the cost of an adult ticket.
Show the worked solution
  • Let aa be the adult ticket price and cc be the child ticket price (in dollars).
  • 7a+4c=73⋯(1)7a + 4c = 73 \quad \cdots (1)
  • 6a+9c=96⋯(2)6a + 9c = 96 \quad \cdots (2)
  • (1)×9:63a+36c=657⋯(3)(1) \times 9: \quad 63a + 36c = 657 \quad \cdots (3)
  • (2)×4:24a+36c=384⋯(4)(2) \times 4: \quad 24a + 36c = 384 \quad \cdots (4)
  • (3)−(4):subtract to eliminate c(3) - (4): \quad \scriptsize\textit{subtract to eliminate } c
  • 39a=27339a = 273
  • a=27339a = \frac{273}{39}

Answer: 77

Questions parents ask

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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