Linear Graphs and Simultaneous 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 equations free

What this topic covers

Worked examples

Example 1

Using the elimination method, solve the simultaneous equations 4x+8y=204x + 8y = 20 and x−2y=−11x - 2y = -11. Find the value of <i>x</i>.
Show the worked solution
  • Labeltheequations:Label the equations:
  • $4x + 8y = 20 \quad \cdots (1)$
  • $x - 2y = -11 \quad \cdots (2)$
  • $(2) \times 4$: make $y$-coefficients equal in magnitude
  • $4x - 8y = -44 \quad \cdots (3)$
  • $(1) + (3)$: eliminate $y \quad \scriptsize\textit{add equations}$
  • $8x = -24$
  • $x = -3$

Answer: −3-3

Example 2

Using the substitution method, solve the simultaneous equations −2x−y=−4-2x - y = -4 and −2x−3y=−16-2x - 3y = -16. Find the value of <i>x</i>.
Show the worked solution
  • Labeltheequations:Label the equations:
  • $-2x - y = -4 \quad \cdots (1)$
  • $-2x - 3y = -16 \quad \cdots (2)$
  • From $(1)$, rearrange to make $y$ the subject: $\quad \scriptsize\textit{rearrange}$
  • $y = -2x + 4 \quad \cdots (3)$
  • Substitute $(3)$ into $(2)$: $\quad \scriptsize\textit{substitute}$
  • $-2x - 3(-2x + 4) = -16$
  • $-2x + 6x - 12 = -16$

Answer: −1-1

Example 3

Kavitha bought 44 pens and 44 notebooks for \40.If. If 6pensand pens and 3notebookscost notebooks cost \5151, find the cost of one pen.
Show the worked solution
  • Let $x$ be the cost of one pen and $y$ be the cost of one notebook (in dollars).
  • $4x + 4y = 40 \quad \cdots (1)$
  • $6x + 3y = 51 \quad \cdots (2)$
  • $(1) \times 3: \quad 12x + 12y = 120 \quad \cdots (3)$
  • $(2) \times 4: \quad 24x + 12y = 204 \quad \cdots (4)$
  • $(3) - (4): \quad \scriptsize\textit{subtract to eliminate } y$
  • $-12x = -84$
  • $x = \frac{-84}{-12}$

Answer: 77

Questions parents ask

Is it really free?

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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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