Translate each into a variable equation AND solve: The sum of two numbers is two. The difference between eight and twice the smaller number is two less than four times the larger. Find the two numbers.
+128474 Let x be the smaller number and y be the larger.....so....
x + y = 2 → y = 2 - x (1)
" The difference between eight and twice the smaller number is two less than four times the larger"
translates as [ 8 - 2x ] + 2 = 4y (2)
Put (1) into (2) and we have that
[8 - 2x ] + 2 = 4 [ 2 - x ] simplify
10 - 2x = 8 - 4x add 4x to both sides, subract 10 from both sides
2x = -2 divide both sides by 2
x = -1
Sub this into (1) to find y
y = 2 - (-1) = 2 + 1 = 3
