Question

ꜱᴏʟᴠᴇ ᴛʜᴇ ꜱʏꜱᴛᴇᴍ ᴏꜰ ᴇQᴜᴀᴛɪᴏɴꜱ.

3(ᴀ+3ʙ)=11ᴀʙ, 3(2ᴀ+ʙ)=7ᴀʙ

ᴅᴏɴᴛ ꜱᴘᴀᴍ❌️​

Answer 1

Answer:

A=1

B=3/2

Step-by-step explanation:

Hope it helps you

Answer 2

$\huge {\boxed {\mathbb {QUESTION}}}$

ꜱᴏʟᴠᴇ ᴛʜᴇ ꜱʏꜱᴛᴇᴍ ᴏꜰ ᴇQᴜᴀᴛɪᴏɴꜱ.

3(ᴀ+3ʙ)=11ᴀʙ, 3(2ᴀ+ʙ)=7ᴀʙ

$\huge {\boxed {\mathbb {ANSWER}}}$

$3(A+3B)=11AB$

$\implies{\boxed {3A+9B=11AB}}$

$3(2A+B)=7AB$

$\implies{\boxed {6A+3B=7AB}}$

$Divide \:all \:variables \:by\: AB$

$\implies \frac{3\cancel {A}}{\cancel {A} B} +\frac{9\cancel {B}}{A\cancel {B}}=\frac{11\cancel {AB}}{\cancel {AB}}$

$\implies \frac{3}{B}+\frac{9}{A}=11$

$\implies{\boxed {3\times(\frac{1}{B})+9\times (\frac{1}{A})=11}}$

$\implies \frac{6\cancel {A}}{\cancel {A} B} +\frac{3\cancel {B}}{A\cancel {B}}=\frac{7\cancel {AB}}{\cancel {AB}}$

$\implies \frac{6}{B}+\frac{3}{A}=7$

$\implies{\boxed {6\times(\frac{1}{B})+3\times (\frac{1}{A})=7}}$

$Let\:\frac{1}{B}\:be\:x\\and\:\frac{1}{A}\:be\:y$

$\implies{\boxed {3x+9y=11}}--(1)$

$\implies{\boxed {6x+3y=7}}--(2)$

$Multiply \:equation \:(1) \:with\:6$

$Multiply \:equation \:(2) \:with\:3$

$\implies 6(3x+9y=11)\\ \implies{\boxed {18x+54y=66}}--(3) \\ \implies 3(6x+3y=7) \\ \implies {\boxed {18x+9y=21}}--(4)$

$Substract\: equation\: (3)\: from\: equation\: (4)\:$

$\cancel {18x} +54y=66\\ \cancel {-18x} -9y=-21$

_______________

$45y=45$

$\implies y=\cancel\frac{45}{45}$

$\implies{\boxed {\boxed {y=1}}}$

$Substitute\:the\:value\:of\:y\:in\:equation \:(1)$

$\implies 3x+9(1)=11$

$\implies 3x+9=11$

$\implies 3x=11-9$

$\implies 3x=2$

$\implies{\boxed {\boxed {x=\frac{2}{3}}}}$

$\implies y=\frac{1}{A}$

$\implies 1=\frac{1}{A}$

$\therefore\implies {\boxed {\boxed {\boxed {\boxed {A=1}}}}}$

$\implies x=\frac{1}{A}$

$\implies \frac{2}{3}=\frac{1}{B}$

$\therefore\implies {\boxed {\boxed {\boxed {\boxed {B=\frac{3}{2}}}}}}$

$\huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

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$\huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$Elimination\:method$

• $Elimination\: method \:you\:either \: add\: or\\ subtract\: the\: equations\: to\: get\: an \:equation \:in\\ one\: variable.$
• $When\: the\: coefficients\: of \:one\: variable\\ are\: opposites\: you\: add\: the\: equations\\ to \:eliminate\: a\: variable\: and\: when\: the\\ coefficients\: of\: one\: variable\: are\: equal\\ you\: subtract\: the\: equations\: to \:eliminate\: a\\ variable.$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$