Systems Of Linear Equations

Question

Two numbers differ by 5. four times the smaller number is 5 lesss than three times the larger. Find the numbers

Answer 1

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

x - y = 5 --> y = x-5

3x-4y = 5

Add -4 times the first equation to the second equation to temporarily eliminate y.

-4x +4y=-20

3x -4y = 5

----------------

-x =-15

x = 15

y = x-5 --> y= 15-5 = 10

Checking

3(15) -4(10) = 45-40 = 5

Answer 2

x - y = 5

4y = 3x - 4