Question

substitute y =2x-7in the equation x-2y= -1
find the value of x and y​

Answer 1

$\large\sf\underline{Given\::}$

• y = 2x - 7

• x - 2y = - 1

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$\large\sf\underline{To\:find\::}$

• Value of x and y

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$\large\sf\underline{How\:to\:proceed\:?}$

In this question firstly we are given y = 2x - 7 . So now we are gonna substitute this value of y in x - 2y = - 1. After substituting we will solve the equation and doing so we would get the value of x. Then after we would substitute the value of x in y = 2x - 7 . Doing this all we will get the value of x and y. Let's begin !

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$\large\sf\underline{Solution\::}$

$\bf\:x-2y=-1$

• Let's substitute the value of y as 2x - 7

$\sf\rightarrow\:x-2(2x-7)=-1$

• Multiplying the terms in LHS

$\sf\rightarrow\:x-4x+14=-1$

• Transposing +14 to other side it becomes -14

$\sf\rightarrow\:x-4x=-1-14$

$\sf\rightarrow\:-3x=-15$

$\sf\rightarrow\:\cancel{-}3x=\cancel{-}15$

$\sf\rightarrow\:3x=15$

• Transposing 3 to other side it goes to the denominator

$\sf\rightarrow\:x=\frac{15}{3}$

• Reducing it to lower terms

$\sf\rightarrow\:x=\cancel{\frac{15}{3}}$

$\small{\underline{\boxed{\mathrm\red{\rightarrow\:x\:=\:5}}}}$ ★

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Now let's substitute the value of x in :

$\bf\:y=2x-7$

• Substituting x as 5

$\sf\to\:y=2(5)-7$

$\sf\to\:y=10-7$

$\small{\underline{\boxed{\mathrm\red{\rightarrow\:y\:=\:3}}}}$ ★

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$\large\sf\underline{Verifying\::}$

Let's check our answers. There are two ways to check our answers. One is to substitute the value of y and x in y = 2x - 7 or by substituting the value of x and y in x - 2y = - 1. However in both the cases we must get LHS = RHS.

$\sf\:y=2x-7$

• Substituting the value of y as 3 and x as 5

$\sf\leadsto\:3=2(5)-7$

$\sf\leadsto\:3=10-7$

$\sf\leadsto\:3=3$

$\bf\leadsto\:LHS=RHS$

$\large{\mathfrak\blue{hence\:verified\:!!}}$

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!! Hope it helps !!