Question

Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smaller number. Let x represent the smaller number and y represent the larger number. Which equations represent this situation?

Answer 1

Let the smaller number be x.
Let the bigger number be y.

$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y- 7 = 2x \tex{ ----- (2) } \end{cases}$

Rearrange equation (2):
$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y = 2x + 7 \tex{ ----- (2) } \end{cases}$


Sub (2) into (1):

$4x + 3(2x + 7 ) = 31$
$4x + 6x + 21 = 31$
$10x + 21 = 31$
$10x = 10$
$x = 1$

Sub x = 1 into (2):

$y = 2x + 7$
$y = 2(1) + 7$
$y= 9$

Answer: The two numbers are 1 and 9.

Answer 2

4x+3y=31

y-7=2x

(y-7)/2=x