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

May 9, 2018

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

#### Explanation:

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

$2 x + 3 y = 13$
$x + y = 7 \implies$ $y = 7 - x$:
$2 x + 3 \left(7 - x\right) = 13$
$2 x + 21 - 3 x = 13$
$x = 8$
$y = 7 - 8 = - 1$

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

May 9, 2018

The numbers are $8$ and $- 1$

#### Explanation:

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

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

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

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

$2 x + 3 \left(7 - x\right)$

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

$2 x + 3 \left(7 - x\right) = 13$

$2 x + 21 - 3 x = 13$

$- x = 13 - 21$

$- x = - 8$

$x = 8$

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

Check:

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