Question

3x - 2y =3 ; 4x +5y = 50

Answer 1

ANSWER:

TO SOLVE:

• 3x - 2y = 3
• 4x + 5y = 50

SOLUTION:

There are many methods of solving pair of linear equations. The most common are substitution method and elimination method.

Method 1: Substitution Method

$:\longrightarrow\sf{3x - 2y = 3----(1)}\\\\:\longrightarrow\sf{4x + 5y = 50}\\\\:\implies\sf{4x=50-5y}\\\\:\implies\sf{x=\dfrac{50-5y}{4}----(2)}\\\\\text{\sf{Putting (2) in (1)}}\\\\:\implies\sf{3\left(\dfrac{50-5y}{4}\right) - 2y = 3}\\\\:\implies\sf{\dfrac{150-15y}{4} - 2y = 3}\\\\:\implies\sf{\dfrac{150-15y-8y}{4}=3}\\\\:\implies\sf{150-23y=12}\\\\:\implies\sf{23y=150-12}\\\\:\implies\sf{23y=138}\\\\:\implies\sf{y=6}$

$:\implies\sf{x=\dfrac{50-5y}{4}=\dfrac{50-5(6)}{4}=\dfrac{50-30}{4}=\dfrac{20}{4}}\\\\:\implies\sf{x=5}\\\\\text{\sf{So,}}\\\\\bf{:\implies x=5\:\:and\:\:y=6}$

Method 2: Elimination Method

$:\longrightarrow\sf{3x-2y=3----(3)}\\\\:\longrightarrow\sf{4x+5y=50----(4)}\\\\\text{\sf{Multiplying equation (3) with 5 \& (4) with 2}}\\\\:\implies\sf{15x-10y=15----(5)}\\\\:\implies\sf{8x+10y=100----(6)}\\\\\text{\sf{This made the magnitude of coefficient of y same in both equations}}\\\\\text{\sf{Due to different signs, we add (5) \& (6)}}\\\\:\implies\sf{(15x-10y)+(8x+10y)=15+100}\\\\:\implies\sf{15x-10y+8x+10y=115}\\\\:\implies\sf{23x=115}\\\\:\implies\sf{x=5}\\\\\text{\sf{Putting value of x in (6)}}$

$:\implies\sf{8(5)+10y=100}\\\\:\implies\sf{40+10y=100}\\\\:\implies\sf{10y=100-40}\\\\:\implies\sf{10y=60}\\\\:\implies\sf{y=6}\\\\\text{\sf{So,}}\\\\\bf{:\implies x=5\:\:and\:\:y=6}$

LEARN MORE:

• In substitution method, we calculate one variable in terms of the other and substitute it in the other equation.
• In elimination method, we eliminate one variable by either adding or subtracting the equations and then putting that value in one of the equation to get value of the other variable.

Answer 2

$\huge{\dag\:{\underline{\boxed{\mathfrak{\purple{Answer}}}}}}$

Let us solve this problem by Substitution Method.

➭3x - 2y =3------(1)

➭4x +5y = 50-----(2)

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➦ Let us take equation (1) 3x - 2y =3

➦ Now make x alone = 3 + 2y /3

➦ So here value of x is 3 + 2y /3

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➳Now substitute this value of x in eq(2).

➦ 4x +5y = 50

➦ 4 ( 3 + 2y /3) + 5y = 50

➦ 12 + 8y + 15y = 150

➦ 23y = 138

➦ y = 6

• So here we got value of y as 6.

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➳ Now let us substitute this value of y in eq(1).

➦ 3x - 2y =3

➦ 3x - 2(6) = 3

➦ 3x = 12 +3

➦ x = 15/3

➦ x = 5

• So here we got value of x as 5.

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Verification;

• Let us put the value of x and y in both the equations.

Equation 1:-

• 3x - 2y =3
• 3(5) - 2(6) = 3
• 15 - 12 = 3
• 3 = 3
• LHS = RHS

Equation 2;

• 4x +5y = 50
• 4(5) - 5(6) = 50
• 20 + 30 = 50
• 50 = 50
• LHS = RHS.

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Hence value of x is 5 and y is 6.