Question

5x-2y=7, -3x+5y=-8 by substitution method​

Answer 1

★ How to do :-

Here, we are given with two equations. We are asked to find the value of x and y using substitution method. By using the first equation we will find the value of x by substituting the values. Then, we use the hint of x and then we can find the value of y. Then we can find the original value of x by using the value of y. Here, we also shift numbers from one hand side to the other which changes it's sign. So, let's solve!!

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➤ Solution :-

${\sf \leadsto 5x - 2y = 7 \: --- (i)}$

${\sf \leadsto -3x + 5y = (-8) \: --- (ii)}$

Find the value of x by first equation.

${\tt \leadsto 5x = 7 + 2y}$

Shift the number 5 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{7 + 2y}{5}}$

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Now, let's find the value of y by second equation.

Value of y :-

${\tt \leadsto -3x + 5y = (-8)}$

Substitute the value of x.

${\tt \leadsto -3 \bigg( \dfrac{7 + 2y}{5} \bigg) + 5y = (-8)}$

Multiply 3 with both numbers in bracket.

${\tt \leadsto \dfrac{-21 - 6y}{5} + 5y = (-8)}$

Convert the variable 5y with same denominator as fraction.

${\tt \leadsto \dfrac{-21 - 6y + 25y}{5} = (-8)}$

Shift the number 5 from LHS to RHS.

${\tt \leadsto -21 - 6y + 25y = (-8) \times 5}$

Multiply the numbers of RHS.

${\tt \leadsto -21 - 6y + 25y = (-40)}$

Shift the number -21 from LHS to RHS, changing it's sign.

${\tt \leadsto 6y + 25y = (-40) + 21}$

Add the values on LHS and RHS.

${\tt \leadsto 19y = (-19)}$

Shift the number 19 from LHS to RHS.

${\tt \leadsto y = \dfrac{(-19)}{19}}$

Simplify the fraction to get the value of y.

${\tt \leadsto y = (-1)}$

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Now, let's find the value of x by first equation.

Value of x :-

${\tt \leadsto 5x - 2y = 7}$

Substitute the value of y.

${\tt \leadsto 5x - 2 (-1) = 7}$

Multiply the numbers on LHS.

${\tt \leadsto 5x - (-2) = 7}$

Write the answer obtained in only one sign.

${\tt \leadsto 5x + 2 = 7}$

Shift the number 2 from LHS to RHS, changing it's sign.

${\tt \leadsto 5x = 7 - 2}$

Subtract the values on RHS.

${\tt \leadsto 5x = 5}$

Shift the number 5 from LHS to RHS.

${\tt \leadsto x = \dfrac{5}{5}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = 1}$

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${\red{\underline{\boxed{\bf So, \: the \: values \: of \: x \: and \: y \: is \: 1 \: and \: (-1) \: respectively.}}}}$