Question

The cost of 2 pencils and 3 erasers is Rupees 9 and
the cost of 4 pencils and 6 erasers is rupees 18. Find
the cost of each pencil and each eraser by substitution method

Answer 1

➤ Answer

• There are infinitely many solution of the given equations.

➤ To Find

• The cost of each pencil and each eraser.

➤ Given

• The cost of 2 pencil and 3 erasers in ₹ 9 and the cost of 4 pencil and 6 eraser is ₹ 18.

➤ Step By Step Explanation

Given the cost of 2 pencil and 3 erasers in ₹ 9 and the cost of 4 pencil and 6 eraser is ₹ 18. We need to find the cost of each pencil and eraser.

So let's do it !!

Assumption

Let the cost of each pencil be x and of each eraser be y. Then the equation will be ⤵

Equations

2x + 3y = 9. - first equation.

4x + 6y = 18. - second equation

Comparing

Let's check whether these equations have a solution or not.

If $\tt\cfrac{a_1}{a_2} \neq\cfrac{b_1}{b_2}$ then the equations will have a unique solution.

If $\sf \cfrac{a_1}{a_2} = \cfrac{b_1}{b_2} \neq \cfrac{c_1}{c_2}$ then the equation will have no solution.

If $\tt \cfrac{a_1}{a_2}=\cfrac{b_1}{b_2} = \cfrac{c_1}{c_2}$ then the equation will have infinitely many solution.

So let's check !!

$\tt\cfrac{a_1}{a_2}=\cfrac{b_1}{b_2} = \cfrac{c_1}{c_2} \\ \\ \cancel\cfrac{2}{4} = \cancel\cfrac{3}{6} = \cancel\cfrac{9}{18} \\ \\ \cfrac{1}{2} = \cfrac{1}{2} = \cfrac{1}{2}$

Therefore, we can find infinitely many solution of the given equations.

Substitution method

So let's find some solutions for the given equations.

Let x = 3 then y will be ⤵

2x + 3y = 9

2(3) + 3y = 9

6 + 3y = 9

3y = 9 - 6

3y = 3

y = 3/3

y = 1

Let x = 1 then y will be ⤵

4x + 6y = 18

4(1) + 6y = 18

6y = 18 - 4

6y = 14

y = 14/6

y = 7/3

Like this we can calculate infinitely many solution of the given equations.

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