# Question #71e99

Nov 30, 2017

22 & 15

#### Explanation:

x + y = 37
x - y = 7
2x = 44
x = 44/2

x = 22 The first number is 22.

22 - y = 7 Since x - y = 7

y = 15 The second number is 15.

Nov 30, 2017

$22$ and $15$.

#### Explanation:

Let the two numbers be $A$ and $B$.

Hence,

$A + B = 37$

$A - B = 7$

Add these two equations. $B$ cancels out

$2 A = 44$

$A = 22$

Replace A in the first equation

$A + B = 37$

$22 + B = 37$

$B = 15$

Sum: $\text{ } 22 + 15 = 37$

Difference: $\text{ } 22 - 15 = 7$

Nov 30, 2017

$22 \text{ and } 15$

#### Explanation:

$\text{let the two numbers be x and y with } x > y$

$x + y = 37 \to \left(1\right)$

$x - y = 7 \to \left(2\right)$

$\text{add the two equations term by term to eliminate y}$

$\left(x + x\right) + \left(y - y\right) = 37 + 7$

$\Rightarrow 2 x = 44$

$\text{divide both sides by 2}$

$\frac{\cancel{2} x}{\cancel{2}} = \frac{44}{2}$

$\Rightarrow x = 22$

$\text{substitute this value into either of the two equations}$

$\text{(1) } \to 22 + y = 37 \Rightarrow y = 37 - 22 = 15$

$\text{note "22+15=37" and } 22 - 15 = 7$