Question

11. The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number, what are the two numbers?

Answer 1

Answer:

Step-by-step explanation:

If you let x stand for the first number and y for the second number, then we were given: x + y = 13 2x - 3y = 1 Solve the equation we get x = 8, y = 5 The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number, the two numbers are: A. x = 8, y = 5

Answer 2

Let the two no.s be x and y

According to the question :-

$\\ \bullet \quad \sf x + y = 13 - - - (1)$

And it is also stated the two times the first no. (2x) minus ( - ) three times the second no. (3y) is equivalent to 1

$\\ \bullet \quad \sf 2x - 3y = 1 - - - (2)$

Now, multiply the entire 1st equation with 2 in order to get the identical coefficients of "x" By doing this we can easily eliminate the x by subtracting the equations and find the value of y

Let's perform this :-

Multiply the 1st equation with 2

$\\ \quad \rightarrow \tt 2(x + y) = 2 \times 13 \\ \\ \quad \rightarrow \boxed{\tt 2x + 2y = 26 }$

Now, Subtract these two equations to find the value of y

$\\ \quad \longrightarrow \tt (2x + 2y) - (2x - 3y) = 26 - 1 \\ \\ \longrightarrow \tt \cancel{ 2x} + 2y - \cancel{2x }+ 3y = 25 \\ \\ \longrightarrow \tt 5y = 25 \\ \\ \quad \longrightarrow \boxed{ \orange{\tt y = 5} } \bigstar$

Now, substitute the value of y in any of the equations to find x. For now, let's substitute it in equation (1)

$\\ \quad \longrightarrow \tt x + y = 13 \\ \\ \quad \longrightarrow \tt x + 5 = 13 \\ \\ \quad \longrightarrow \boxed{ \orange{ \tt x = 8} }\bigstar$

$\\ \therefore \underline{ \sf the \: required \: no.s \: are \: \bold{5} \: and \: \bold{8}.}$

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