Question

the sum of two numbers is 4 less than twice the larger. if the large is decreased by three times the smaller, the result is -20.

Answer 1

let x be the larger number and y be the smaller number.

Eq'n 1: x + y = 4 - 2x

Simplify...

x + 2x = 4 - y
3x = 4 - y
y = 3x - 4


Eq'n 2: x - 3y = -20

Plugging in the y from the Eq'n 1.

x - 3(3x -4) = -20
x - 9x + 12 = -20
-8x = -20 - 12
-8x = -32

x = 4

now we have the x, for us to get the y, we have to substitute the x from any of the 2 Eq'ns above.

x + y = 4 - 2x
so if x = 4

4 + y = 4 - 2(4)
4 -4 + y = -8
y = -8

so we can say the larger number "x" is 4 and the smaller one which is "y" is -8