$\def\D{\displaystyle}$

1 (CIE 2012, s, paper 12, question 4)

Solve the simultaneous equations

$\D 5x + 3y = 2$ and $\D \frac{2}{x}-\frac{3}{y}=1.$

[5]

2 (CIE 2012, w, paper 22, question 1)

Solve the equation $\D |7x + 5| = |3x – 13|.$ [4]

3 (CIE 2012, w, paper 23, question 1)

Solve the equation $\D |5x + 7| = 13.$ [3]

4 (CIE 2015, s, paper 22, question 5)

Solve the simultaneous equations

$\D \begin{array}{rcl}

2x^2+3y^2&=&7y,\\x+y&=&4.

\end{array}$

[5]

5 (CIE 2016, w, paper 21, question 1)

Solve the equation $\D |4x - 3 |= x.$ [3]

6 (CIE 2017, march, paper 22, question 1)

Solve the equation $\D |5 - 3x |= 10.$ [3]

7 (CIE 2017, s, paper 22, question 1)

Solve $\D |5x + 3 |= |1 - 3x |.$ [3]

8 (CIE 2017, w, paper 21, question 4)

Solve the following simultaneous equations for $\D x$ and $\D y,$ giving each answer in its simplest surd form.

$\D \begin{array}{rcl}

\sqrt{3}x + y& =& 4\\

x - 2y &=& 5 \sqrt{3}

\end{array} $

[5]

9 (CIE 2017, w, paper 22, question 1)

If $\D z = 2 + \sqrt{3}$ find the integers $\D a$ and $\D b$ such that $\D az^2 + bz = 1 + \sqrt{3}.$ [5]

10 (CIE 2017, w, paper 22, question 3)

Solve the inequality $\D |3x - 1|> 3 + x.$ [3]

11 (CIE 2017, w, paper 23, question 2)

Solve the equation $\D |3x - 1| = |5 + x| .$ [3]

12 (CIE 2018, s, paper 11, question 1)

Solve the equations

$\D \begin{array}{rcl}

y - x &=& 4,\\

x^2 + y^2 - 8x - 4y - 16 &=& 0.

\end{array}$

[5]

$\D x = 4; y = -6$

2. $\D x = 0.8;-4.5$

3. $\D 1.2,-4$

4. $\D x = \frac{4}{3},

\frac{8}{3}$

$\D x = 3; y = 1$

5. $\D x = 1; 0.6$

6. $\D -5/3; 5$

7. $\D x = -2; x = -0.25$

8. $\D x = 2 +\sqrt{3},y=1-2\sqrt{3}$

9. $\D a = 1; b = -3$

10. $\D x > 2; x < -.5$

11. $\D x = -1$

12. $\D x = 4; y = 8$

$\D x = -2; y = 2$

1 (CIE 2012, s, paper 12, question 4)

Solve the simultaneous equations

$\D 5x + 3y = 2$ and $\D \frac{2}{x}-\frac{3}{y}=1.$

[5]

2 (CIE 2012, w, paper 22, question 1)

Solve the equation $\D |7x + 5| = |3x – 13|.$ [4]

3 (CIE 2012, w, paper 23, question 1)

Solve the equation $\D |5x + 7| = 13.$ [3]

4 (CIE 2015, s, paper 22, question 5)

Solve the simultaneous equations

$\D \begin{array}{rcl}

2x^2+3y^2&=&7y,\\x+y&=&4.

\end{array}$

[5]

5 (CIE 2016, w, paper 21, question 1)

Solve the equation $\D |4x - 3 |= x.$ [3]

6 (CIE 2017, march, paper 22, question 1)

Solve the equation $\D |5 - 3x |= 10.$ [3]

7 (CIE 2017, s, paper 22, question 1)

Solve $\D |5x + 3 |= |1 - 3x |.$ [3]

8 (CIE 2017, w, paper 21, question 4)

Solve the following simultaneous equations for $\D x$ and $\D y,$ giving each answer in its simplest surd form.

$\D \begin{array}{rcl}

\sqrt{3}x + y& =& 4\\

x - 2y &=& 5 \sqrt{3}

\end{array} $

[5]

9 (CIE 2017, w, paper 22, question 1)

If $\D z = 2 + \sqrt{3}$ find the integers $\D a$ and $\D b$ such that $\D az^2 + bz = 1 + \sqrt{3}.$ [5]

10 (CIE 2017, w, paper 22, question 3)

Solve the inequality $\D |3x - 1|> 3 + x.$ [3]

11 (CIE 2017, w, paper 23, question 2)

Solve the equation $\D |3x - 1| = |5 + x| .$ [3]

12 (CIE 2018, s, paper 11, question 1)

Solve the equations

$\D \begin{array}{rcl}

y - x &=& 4,\\

x^2 + y^2 - 8x - 4y - 16 &=& 0.

\end{array}$

[5]

### Answers

1. $\D x = \frac{1}{5},y=\frac{1}{3}$:$\D x = 4; y = -6$

2. $\D x = 0.8;-4.5$

3. $\D 1.2,-4$

4. $\D x = \frac{4}{3},

\frac{8}{3}$

$\D x = 3; y = 1$

5. $\D x = 1; 0.6$

6. $\D -5/3; 5$

7. $\D x = -2; x = -0.25$

8. $\D x = 2 +\sqrt{3},y=1-2\sqrt{3}$

9. $\D a = 1; b = -3$

10. $\D x > 2; x < -.5$

11. $\D x = -1$

12. $\D x = 4; y = 8$

$\D x = -2; y = 2$

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