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Question

Solve for a and b $$\displaystyle 2\left ( a+b \right )-\left ( a-b \right )=6,\: 4\left ( a-b \right )=2\left ( a+b \right )-9 $$


A
a=34,b=134
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B
a=12,b=112
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C
a=134,b=34
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D
a=32,b=34
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Solution

The correct option is C $$\displaystyle a=\frac{3}{4},b=1\frac{3}{4}$$
Given,
$$2\left( a+b \right) -\left( a-b \right) =6$$
$$4\left( a-b \right) =2\left( a+b \right) -9$$
$$2\left( a+b \right) -\left( a-b \right) =6$$
$$2a+2b-a+b=6$$
$$a+3b=6$$ ........ $$(1)$$
$$4\left( a-b \right) =2\left( a+b \right) -9$$
$$4a-4b=2a+2b-9$$
$$2a-6b=-9$$ ...... $$(2)$$
On adding equations $$(1)$$ and $$(2)$$, we get
$$2a+6b=12$$
 $$2a-6b=-9$$
__________________
$$4a=3$$
 $$a=\dfrac { 3 }{ 4 } $$
Putting the value of $$a$$ in eq $$(1)$$, we get
$$\dfrac { 3 }{ 4 } +3b=6$$
$$3b=6-\dfrac { 3 }{ 4 } $$
$$b=\dfrac { 21 }{ 4 } \times \dfrac { 1 }{ 3 } =\dfrac { 21 }{ 12 } =1\dfrac { 9 }{ 12 } =1\dfrac { 3 }{ 4 } $$
Hence, $$a=\dfrac { 3 }{ 4 } $$ and $$b=1\dfrac { 3 }{ 4 } $$

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