Two times a number plus three times another number equals 13.The sum of the two numbers is 7.What are the numbers?

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Two times a number plus three times another number equals 13.The sum of the two numbers is 7.What are the numbers?

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Answer 1 · 2018-05-09T07:14:28

The two numbers are $8$ $8$ and $- 1$ $-1$

Explanation:

Let $x$ $x$ and $y$ $y$ be the numbers:

$2 x + 3 y = 13$ $2x+3y=13$
$x + y = 7 \Rightarrow$ $x+y=7=>$ $y = 7 - x$ $y=7-x$ :
$2 x + 3 (7 - x) = 13$ $2x+3(7-x)=13$
$2 x + 21 - 3 x = 13$ $2x+21-3x=13$
$x = 8$ $x=8$
$y = 7 - 8 = - 1$ $y=7-8=-1$

Check:
$2 \cdot 8 + 3 \cdot (- 1) = 16 - 3 = 13$ $2*8+3*(-1)=16-3=13$
$8 - 1 = 7$ $8-1=7$

Answer 2 · 2018-05-09T07:24:00

The numbers are $8$ $8$ and $- 1$ $-1$

Explanation:

You can solve this by using $2$ $2$ variables and making two simultaneous equations.

But we know the relationship between the two numbers (they add to $7$ $7$ ) so it is possible to use one variable.

Let one number be $x$ $x$ . The other number is $7 - x$ $7-x$

Write an expression for "Two times one number plus three times the other number:"

$2 x + 3 (7 - x)$ $2x + 3(7-x)$

Make an equation: The sum is equal to $13$ $13$

$2 x + 3 (7 - x) = 13$ $2x + 3(7-x) =13$

$2 x + 21 - 3 x = 13$ $2x+21-3x=13$

$- x = 13 - 21$ $-x = 13-21$

$- x = - 8$ $-x = -8$

$x = 8$ $x=8$

If one number is $8$ $8$ , the other number is $7 - 8 = - 1$ $7-8 =-1$

Check:

$2 \times 8 + 3 \times (- 1)$ $2 xx 8 + 3xx(-1)$
$= 16 - 3$ $=16-3$
$= 13$ $=13$

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Two times a number plus three times another number equals 13.The sum of the two numbers is 7.What are the numbers?

2 Answers

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