The larger number is 10 and smaller number is 6.
Step-by-step explanation:
Given,
The difference between two numbers = 4
Let,
x be the larger number.
y be the smaller number.
According to given statement;
x-y=4 Eqn 1
3y=2x-2 Eqn 2
Multiplying Eqn 1 by 3
[tex]3(x-y=4)\\3x-3y=12\ \ \ Eqn\ 3[/tex]
Putting value of 3y from Eqn 2 in Eqn 3
[tex]3x-(2x-2)=12\\3x-2x+2=12\\x=12-2\\x=10[/tex]
Putting x = 10 in Eqn 2
[tex]3y=2(10)-2\\3y=20-2\\3y=18[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{18}{3}\\y=6[/tex]
The larger number is 10 and smaller number is 6.
Keywords: linear equation, substitution method
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