Answer:
x = 5 and y = 7
This implies that the value of the first number is 5 and the value of the second number is 7
Explanation:
To find the numbers, we need to interpret the question into an equation.
let x be the first number and y be the second number.
The first statement in the question: "One number is two less than a second number" can be mathematically written as:
x = y- 2 -----------------------------------------------------(1)
The next statement: "Five times the first is 4 more than 3 times the second" can be mathematically written as
5x = 4 + 3y ---------------------------------------------------(2)
We can solve the two equations either by elimination method or substitution method or both method.
But we are going to use substitution method to solve the system of the equation.
x = y- 2 ---------------------------------------------------------(1)
5x = 4 + 3y ---------------------------------------------------(2)
Substitute equation (1) into equation (2)
5 (y -2) = 4 + 3y
Open the bracket at the left-hand side of the equation by multiplying all the value in the bracket by 5
5y - 10 = 4+3y
subtract 3y from both-side of the equation
5y - 3y - 10 = 4 + 3y - 3y
5y - 3y - 10 = 4
2y - 10 = 4
Add 10 to both-side of the equation
2y - 10 + 10 = 4 + 10
2y =14
Divide both-side of the equation by 2
2y/2 = 14/2
y = 7
Substitute y = 7 into equation (1)
x = y- 2
x = 7 - 2
x = 5
x = 5 and y = 7
This implies that the value of the first number is 5 and the value of the second number is 7