c)
[tex]\begin{cases}4x - 7y = 3 | \times 2 \\ 3x + 14y = 5 \end{cases}[/tex]
[tex]\begin{cases} 8x - 14y = 6 \\ 3x + 14y = 5\end{cases}[/tex]
[tex]8x + 3x = 6 + 5 \\ 11x = 11 | \div 11 \\ x = 1[/tex]
[tex]3 \times 1 + 14y = 5 \\ 3 + 14y = 5 \\ 14y = 2 | \div 14 \\ y = \frac{2}{14} = \frac{1}{7} [/tex]
[tex]\begin{cases} x = 1 \\ y = \frac{1}{7} \end{cases}[/tex]
d)
[tex]\begin{cases}5x - 2y = 16 | \times 5 \\ 3x + 5y = - 9 | \times 2\end{cases}[/tex]
[tex]\begin{cases}25x - 10y = 80 \\6x + 10y = - 18 \end{cases}[/tex]
[tex]25x + 6x = 80 + ( - 18) \\ 31x = 62 | \div 31 \\ x = 2[/tex]
[tex]5 \times 2 - 2y = 16 \\ 10 - 2y = 16 \\ - 2y = 6 | \div ( - 2) \\ y = - 3[/tex]
[tex]\begin{cases} x = 2 \\ y = - 3\end{cases}[/tex]
e)
[tex]\begin{cases}10x + 21y = - 9 \\ - 5x - 7y = 8 | \times 2 \end{cases}[/tex]
[tex]\begin{cases} 10x + 21y = - 9 \\ - 10x - 14y = 16\end{cases}[/tex]
[tex]21y + ( - 14y) = - 9 + 16 \\ 7y = 7 | \div 7 \\ y = 1[/tex]
[tex]10x + 21 \times 1 = - 9 \\ 10x + 21 = - 9 \\ 10x = - 30 | \div 10 \\ x = - 3[/tex]
[tex]\begin{cases}x = - 3 \\ y = 1 \end{cases}[/tex]
f)
[tex]\begin{cases} 2x + 3y = - 3.5 | \times 2 \\ 3x - 2y = 4.5 | \times 3\end{cases}[/tex]
[tex]\begin{cases}4x + 6y = - 7 \\ 9x - 6y = 13.5 \end{cases}[/tex]
[tex]4x + 9x = - 7 + 13.5 \\ 13x = 6.5 | \div 13 \\ x = \frac{6.5}{13} [/tex]
[tex]x = 0.5[/tex]
[tex]2 \times 0.5 + 3y = - 3.5 \\ 1 + 3y = - 3.5 \\ 3y = - 4.5 | \div 3 \\ y = - \frac{4.5}{3} \\ y = - 1.5[/tex]
[tex]\begin{cases} x = 0.5 \\ y = - 1.5\end{cases}[/tex]
