Răspuns:
[tex]\boxed{\bf a =\dfrac{420}{43}}[/tex]
[tex]\boxed{\bf b = \dfrac{300}{43}}[/tex]
Explicație pas cu pas:
Salutare!
[tex]\it~~~[/tex]
[tex]\bf \dfrac{a}{b}=\dfrac{7}{5} \implies\boxed{\bf 5a = 7b}[/tex]
[tex]\bf 4a+3b = 60[/tex]
Vom inmulti prima relatie cu 4 si a doua relatie cu 5
[tex]\bf 5a = 7b~~\bigg|\cdot4 \implies \boxed{\bf 20a =28b}[/tex]
[tex]\bf 4a+3b = 60~~\bigg|\cdot5\implies \boxed{\bf20a+15b=300}[/tex]
Inlocuim pe 20a in a doua relatie
[tex]\bf 28b+15b = 300\implies43b = 300\implies \boxed{\boxed{\bf b = \dfrac{300}{43} }}[/tex]
[tex]\bf 5a = 7\cdot \dfrac{300}{43}\implies 5a = \dfrac{2100}{43}\implies43\cdot50= 2100[/tex]
[tex]\bf \implies 43\cdot a= 420\implies \boxed{\boxed{\bf a =\dfrac{420}{43} }}[/tex]
[tex]\it~~~~[/tex]
[tex]\it Verificare:[/tex]
[tex]\it \dfrac{a}{b}=\dfrac{\dfrac{420}{43} }{\dfrac{300}{43}} =\dfrac{420}{43}:\dfrac{300}{43}=\dfrac{\not420}{\not43}\cdot\dfrac{\not43}{\not300}=\dfrac{7}{5}~(adevarat)[/tex]
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