Verified answer

SUBSTITUTION METHOD

[tex]\color{royalblue}┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉┉[/tex]

1.[tex]\begin{gathered} \begin{cases} y = 5x \\ x  +  y = 24 \end{cases} \quad \begin{aligned}  \end{aligned} \end{gathered}[/tex]

[tex]\large{\bold{\sf{{x+5x=24 }}}}[/tex]

[tex]\small{\bold{\sf{{x=4 }}}}[/tex]

[tex]\small{\bold{\sf{{ 4+y=24}}}}[/tex]

[tex]\small{\bold{\sf{{ y=24-4}}}}[/tex]

[tex]\small{\bold{\sf{{y=20 }}}}[/tex]

[tex]\large{\bold\color{orange}{\pmb{{\begin{gathered} \begin{cases} x = 4   \\   y = 20 \end{cases} \quad \begin{aligned}  \end{aligned} \end{gathered}}}}}[/tex]

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2.[tex]\begin{gathered} \begin{cases} a+b  = 12   \\   3a + b-8 \end{cases} \quad\begin{aligned}  \end{aligned} \end{gathered}[/tex]

[tex]\small{\bold{\sf{{a + b - (3a + b) = 12 - 8 }}}}[/tex]

[tex]\small{\bold{\sf{{a + b - 3a - b = 12 - 8 }}}}[/tex]

[tex]\small{\bold{\sf{{a - 3a = 12 - 8 }}}}[/tex]

[tex]\small{\bold{\sf{{a = - 2 }}}}[/tex]

[tex]\small{\bold{\sf{{-2 + b = 12}}}}[/tex]

[tex]\small{\bold{\sf{{b=12+2}}}}[/tex]

[tex]\small{\bold{\sf{{b=14}}}}[/tex]

[tex]\large{\bold{\pmb{{\begin{gathered} \begin{cases} a  = -2  \\  b = 14\end{cases}\quad\begin{aligned}  \end{aligned} \end{gathered}}}}}[/tex]

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3.[tex]\begin{gathered} \begin{cases} m=3n-4  \\  m+ n = 12\end{cases} \quad \begin{aligned}  \end{aligned} \end{gathered}[/tex]

[tex]\large{\bold{\sf{{3n-4+ n = 12}}}}[/tex]

[tex]\small{\bold{\sf{{4n-4=12}}}}[/tex]

[tex]\small{\bold{\sf{{4n= 12 + 4}}}}[/tex]

[tex]\small{\bold{\sf{{n =  \frac{16}{4} }}}}[/tex]

[tex]\small{\bold{\sf{{n=4}}}}[/tex]

[tex]\small{\bold{\sf{{m+ 4 = 12}}}}[/tex]

[tex]\small{\bold{\sf{{m = 12-4}}}}[/tex]

[tex]\small{\bold{\sf{{m=8}}}}[/tex]

[tex]\large{\bold\color{green}{\pmb{{\begin{gathered} \begin{cases} m = 8 \\ n = 4\end{cases} \quad \begin{aligned}  \end{aligned} \end{gathered} }}}}[/tex]

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4.[tex]\begin{gathered} \begin{cases} 3 x - 4 y = 0 \\ 2 x + y = 33\end{cases} \quad \begin{aligned}  \end{aligned}\end{gathered}[/tex]

[tex]\small{\bold{\sf{{3x - 4(33 - 2x) = 0}}}}[/tex]

[tex]\small{\bold{\sf{{3x-132+8x= 0}}}}[/tex]

[tex]\small{\bold{\sf{{11x-132 = 0}}}}[/tex]

[tex]\small{\bold{\sf{{11x = 132}}}}[/tex]

[tex]\small{\bold{\sf{{x =  \frac{132}{11} }}}}[/tex]

[tex]\small{\bold{\sf{{x=12}}}}[/tex]

[tex]\small{\bold{\sf{{y = 33-2×12}}}}[/tex]

[tex]\small{\bold{\sf{{y = 9}}}}[/tex]

[tex]\large{\bold\color{royalblue}{\pmb{{\begin{gathered} \begin{cases} x = 12 \\ y = 9\end{cases} \quad \begin{aligned}  \end{aligned} \end{gathered} }}}}[/tex]

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♨[tex]\large{\bold{\sf{{CarryOnLearningヅ}}}}[/tex]