Question

solve by substitution method
6p+3q=6
2p+4q=5​

Answer 1

Answer:

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Answer 2

Answer:

The solution of the given simultaneous equations is

$\displaystyle{\boxed{\red{\sf\:(\:p\,,q\:)\:=\:\left(\:\dfrac{1}{2}\:,\:1\:\right)\:}}}$

Step-by-step-explanation:

The given simultaneous equations are

6p + 3q = 6 - - - ( 1 ) &

2p + 4q = 5 - - - ( 2 )

By dividing equation ( 1 ) by 3, we get,

6p + 3q = 6 - - - ( 1 )

⇒ 2p + q = 2

⇒ q = 2 - 2p

By substituting value of q in equation ( 2 ), we get,

2p + 4q = 5 - - - ( 2 )

⇒ 2p + 4 * ( 2 - 2p ) = 5

⇒ 2p + 8 - 8p = 5

⇒ 2p - 8p = 5 - 8

⇒ - 6p = - 3

⇒ 6p = 3

$\displaystyle{\implies\sf\:p\:=\:\dfrac{3}{6}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:p\:=\:\dfrac{1}{2}}}}}$

Now, by using the value of p,

q = 2 - 2p

$\displaystyle{\implies\sf\:q\:=\:2\:(\:1\:-\:p\:)}$

$\displaystyle{\implies\sf\:q\:=\:2\:\left(\:1\:-\:\dfrac{1}{2}\:\right)}$

$\displaystyle{\implies\sf\:q\:=\:\cancel{2}\:\times\:\dfrac{1}{\cancel{2}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:q\:=\:1\:}}}}$

∴ The solution of the given simultaneous equations is

$\displaystyle{\boxed{\red{\sf\:(\:p\,,q\:)\:=\:\left(\:\dfrac{1}{2}\:,\:1\:\right)\:}}}$