The larger number is 15 and the smaller number is 9.
What is substitution method?
In order to solve a system of equations, the substitution method is typically used in mathematics. This approach involves first solving the equation for one variable, then changing the value of the variable in the second equation.
Suppose
'a' be the larger number and 'b' be the smaller number.
As the difference of two numbers is 6.
⇒ a - b = 6 ..(1)
As two times the smaller is 3 more than the larger.
⇒ 2b = 3 + a ..(2)
From equation (2),
a = 2b - 3
Substitute the value of 'a' in equation (1)
2b - 3 - b = 6
b - 3 = 6
b = 6 + 3
b = 9
Substitute b = 9 in equation (1),
a - 9 = 6
a = 6 + 9
a = 15
Hence, the larger number is 15 and the smaller number is 9.
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