Question

simultaneous equation 3x-5y=15;2x-y= -4​

Answer 1

Answer:

Given :-

• 3x - 5y = 15
• 2x - y = - 4

To Find :-

• What is the value of x and y.

Method Used :-

• Substitution Method.

Solution :-

Given equation :-

$\sf \bold{\green{\dashrightarrow \sf 3x - 5y =\: 15\: ------\: (Equation\: No\: 1)}}$

$\sf \bold{\green{\dashrightarrow \sf 2x - y =\: - 4\: ------\: (Equation\: No\: 2)}}$

Now, from the equation no 2 we get,

$\implies \sf 2x - y =\: - 4$

$\implies \sf 2x =\: - 4 + y$

$\implies \sf\bold{\purple{2x =\: - 4 + y}}$

Now, by putting the value of x in the equation no 2 we get,

$\implies \sf 2x - y =\: - 4$

$\implies \sf 2(- 4 + y) - y =\: - 4$

$\implies \sf - 8 + 2y - y =\: - 4$

$\implies \sf - 8 - y =\: - 4$

$\implies \sf - y =\: - 4 + 8$

$\implies \sf - y =\: 4$

$\implies \sf\bold{\red{y =\: - 4}}$

Again by putting y = - 4 in the equation no 1 we get,

$\implies \sf 3x - 5y =\: 15$

$\implies \sf 3x - 5(- 4) =\: 15$

$\implies \sf 3x + 20 =\: 15$

$\implies \sf 3x =\: 15 - 20$

$\implies \sf 3x =\: - 5$

$\implies \sf\bold{\red{x =\: \dfrac{- 5}{3}}}$

$\therefore$ The value of x is - 4 and the value of y is - 5/3.

Answer 2

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

Equation 1 :

• 3x - 5y = 15

Equation 2 :

• 2x - y = -4

‎

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

• The values of x and y

‎

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

Simultaneous equation can be solved by three methods those are elimination method , comparison method , and substitution method . So I would like to go for elimination method .

In this method we need to first make sure that the leading coefficient of two equations are same. If it is not same we need to make it same by multiplying with suitable numbers. Secondly we need to subtract equation (ii) from equation (i) . Doing so we would get the value of y and then substituting the value of y in any of the two equation we would get the value of x. I hope am clear now , Let's begin !

‎

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

Given Equations :

• 3x - 5y = 15 [equation i]

• 2x - y = -4 [equation ii]

‎

Now let's multiply ( equation i ) by 2 and ( equation ii ) by 3 .

• 3x - 5y = 15 [equation i] × 2

• 2x - y = -4 [equation ii] × 3

‎ After multiplying we get :

• 6x - 10y = 30 [equation i]

• 6x - 3y = -12 [equation ii]

‎

Now subtracting [equation ii] from [equation i] :

$\sf\:equation~(i)~-~equation~(ii)$

Subtraction of equations should be done as :

• LHS - LHS = RHS - RHS

$\sf\implies\:6x-10y-(6x-3y)=30-(-12)$

• Now multiplying and removing the brackets

$\sf\implies\:6x-10y-6x+3y=30+12$

• Arranging the like terms

$\sf\implies\:6x-6x-10y+3y=42$

• Carrying out simple calculation on like terms , like terms with opposite signs gets cancelled out

$\sf\implies\:\cancel{6x}-\cancel{6x}-10y+3y=42$

$\sf\implies\:-10y+3y=42$

$\sf\implies\:-7y=42$

• Transposing -7 to RHS it goes to the denominator

$\sf\implies\:y=\frac{42}{-7}$

• Reducing the fraction to lower terms

$\sf\implies\:y=\cancel{\frac{42}{-7}}$

$\small{\underline{\boxed{\mathrm\red{\implies\:y~=~-6}}}}$ ★

‎

Now substituting the value of y as ( - 6 ) in [equation i] :

Equation (i) : 6x - 10y = 30

$\sf\implies\:6x-10(-6) =30$

$\sf\implies\:6x-(-60) =30$

$\sf\implies\:6x+60 =30$

• Transposing +60 to RHS it becomes -60

$\sf\implies\:6x =30-60$

$\sf\implies\:6x =-30$

• Transposing 6 to RHS it goes to the denominator

$\sf\implies\:x =\frac{-30}{6}$

• Reducing the fraction to lower terms

$\sf\implies\:x=\cancel{\frac{-30}{6}}$

$\small{\underline{\boxed{\mathrm\red{\implies\:x~=~-5}}}}$ ★

‎

‎

So we got :

• x = ( - 5 ) and

• y = ( - 6 )

‎

Verifying :

Now let's check if our answers are correct. In order to do so we would substitute both the values of x and y in any of the two equation. Doing so if we get LHS = RHS, our answers would be correct.

Taking [equation i] :

$\sf\:6x-10y=30$

• Substituting the values of x and y

$\sf\to\:6(-5)-10(-6)=30$

• Multiplying and removing the brackets

$\sf\to\:(-30)-(-60)=30$

$\sf\to\:-30+60=30$

$\sf\to\:30=30$

$\bf\to\:LHS~=~RHS$

$\small\fbox\blue{Hence~Verified~!! }$

___________________________

Required anSwers :

• Value of x = ( - 5 )

• Value of y = ( - 6 )

‎ ‎

!! Hope it helps !!